It's not a contradiction when willed as Kant even says that it's possible that such a law can be universalized: "it is possible that a universal law of nature might exist in accordance with that maxim"... it really is possible to imagine a world where everyone kept to themselves and no one helped any one else out.

However, it is a contradiction in practice: if you needed help, wouldn't you ask for help? If you needed "love and sympathy of others" (and there definitely has been times when you needed it, don't lie), you're not going to get it if you will this maxim.

Right, this sort of contradiction in practice though strikes me as consequential or inclinational (conditional not absolute concerns), two things that Kant appeared to say were essentially irrelevant to morality/rationality (for instance, in his inn keeper e.g.).

It seems to me that this example doesn't fit well (or too consistent) with the rest of the groundwork and its anti-utilitarian bent. That's my reason for bringing up this example, not a curmudgeonly reaction against being charitable or caring to others.

Well, even Kant understood the need to create maxims that work in practice, or "Practical Maxims", as he called it in the Critique of Practical Reason:

What Kant actually meant is: If anyone used that maxime it would be ineffectual to achieve that end.

Kant has two contradiction types: Contradiction in Conception and Contradiction in the Will

Contradiction in Conception

This is where you cannot conceive a world in which the maxim can be universalized. So concepts implode, the world is messy and confused; it's tantamount, as far as Kant is concerned, to getting "I am wearing a shirt and I am not wearing a shirt". Patent contradictions of this sort are irrational, and you should not act from contradictory maxims for morality, as Kant argues, is grounded in rationality. Acting on contradictions is irrational.

To take a conception of contradiction from Wittgenstein: A contradiction is where nothing is possible. It is not possible for a contradiction to be true. In a way, a world with one contradiction becomes a contradictory world. If the contradiction were part of the world as a logical whole, the whole would cease to be.

That bit you know, I'm sure.

Contradiction in the Will

This is what many of you have been calling "contradiction in practice." It's not the consequences of it that make it immoral. However, what is important is your own moral character. Would your character, picture yourself as a moral actor, act like that consistently? If you conclude with an emphatic No! you have a contradiction in the will. You cannot consistently will such a maxim.

If I will to have a beverage, I grab it any time I will it. But what about something disgusting that is unpleasing to my taste? Well, I could certainly will to taste it on a dare, perhaps, but would I consistently will to taste it--put it in my mouth and chew on it? Even outside of the dare? Clearly the dare is an attempt to force me to do something "contradictory" to my "nature" (the nature of my preferences). A contradiction in the will is where I cannot consistently will the maxim: so picture your future self, if you can, in a similar situation. Would you do the same? And again? Again? Again? Again? Do you see something about this pattern that you do not like? Then don't will it.

Granted, this description looks dangerously close to the contradiction in conception because, well, all those "again"'s seem in principle infinitely enumerable. But hey, you will die some day (fact of your biology), so factor that in too. Perhaps these biological facts prevent this description from just being a "global" or "conceivability" issue.

Types of Duties

Contradictions in conception produces perfect duties: it is your duty to never act on maxims which yield contradictions in conception. You must, as rationality and morality demand, do the opposite.

Contradictions in the will yield imperfect duties. Imperfect duties always yield to perfect duties. There can be no conflicts between them. Imperfect duties do not require that you always act on them. But, at the same time, it is not allowed to consistently ignore them. If you always fail to help others or the poor, you end up willing what you actually don't see as constituting part of your moral character. So you should act from imperfect duties some of the time. It's like moral balancing, I suppose, or similar to Aristotle's "Golden Mean."

1. It's clear (to me at least) what Kant's getting at is the good old Golden Rule, which has been repeated in more or less the same form in Christianity, Islam, Buddhism, Hinduism, and Confucianism (and so on and so forth). Thus Kant's maxim is clearly both a practical maxim and a philosophical one. (The Golden Rule says it better, though, IMO.)

2. Correct me if I'm wrong, but I thought that Kant's moral system was basically that if I conceived of an action that had positive consequences and its antithesis (i.e., nonaction in that situation) had negative consequences, then the correct course to take would be to engage in that action? That is, Bentham/Mill's criticism is simply a restatement of Kant's morality?

To start, a disclaimer: I'm not a Kantian or a Kant expert. I'm a Plato person.

Perhaps Kant means to try to explain an idea that he has, which is an idea that is similar to what is said in Plato's Republic. (Regardless of whether Kant had read Plato or not. People can have similar ideas independently of one another. Also, Kant was obviously influenced by Christianity and defers to "Scripture" on several occasions, and it's also a fact that some of the core beliefs of Christianity was at least indirectly influenced by Plato; perhaps Jesus himself was a kind of Jewish Platonist.) And so, I'll include a little bit of Plato and explicate the concept presented there, and then come back to Kant. But, I'll start by telling you where I'm going with this.

My view is that: I think it's not consequentialist -- if you read Kant in a certain way.

That last line seems important to me, where he says, "he would deprive himself of all hope of the aid he desires." (Of course, I don't know what else is sandwiched around this quote that you placed here. I'm just offering a reasonable way to understand Kant, if he is to be not to be contradictory in an obviously petty way.) Now, writing often lacks the intonational emphasis of regular speech. I think that this can cause confusion sometimes. For a non-consequentialistic reading, try placing the emphasis is on the "hope" part rather than on the "aid" part -- with the phrase, "of the aid he desires," just simply being there to give substantiality to "hope".

In order to capture the right "feel," perhaps a quote from Plato might help (I apologize that I might be taking you away from Kant):

[Cephalus speaking to Socrates]
"But someone who knows he has not been unjust has sweet good hope as his constant companion -- a nurse to his old age, as Pindar says. For he puts it charmingly Socrates, when he says that when someone lives a just and pious life,
Sweet hope is in his heart
Nurse and companion to his age
Hope, captain of the ever-twisting
Mind of mortal men.
How amazingly well he puts that. It is in this connection I would say the possession of wealth is most valuable, not for every man, but for a good and orderly one. Not cheating someone even unintentionally, not lying to him, not owing a sacrifice to some god or money to a person, and as a result departing for that other place in fear -- the possession of wealth makes no small contribution to this. It has many other uses, too, but putting one thing against the other, Socrates, I would say that for a man with any sense, that is how wealth is most useful." (Republic, 331a-b)

The point illustrated here by Plato is that when a person does "good" deeds (eg, acts out of good-will or at least not-intending-to-harm), they have no reason to think that others will want to harm them, at least by means of revenge.
A couple other points will help:
(a) Based on text elsewhere in the Republic (which I won't cite here), Plato suggests the notion that it is "worse" to commit harm, than it is to be harmed.
(b) The sort of "better" and "worse" in (a) has to do with the state of the soul/story of the individual. And a person's "inner-story" sort of depends on what-they-think-of-themselves, and/or what they think that they deserve or are owed -- some might call it having a conscience, or something like that.
(c) One major tenet of Socratic philosophy is that we can't presume to "know" what other people are thinking or intending, without examining them on their own terms. (That is why he asks them so many questions.) For Socrates, "knowing" is a conscious state that necessarily requires carnal actuality; it's not a mere storage of a bunch of data in our heads (ie, a conscious state without carnal actuality). So, Socratic "knowledge" is a kind of technical term, since most people (following Aristotle's way of usage) consider "knowing" to be the latter sort.
(d) For Plato, "good" is what is arising out of knowledge. "Bad" is what arises out of ignorance. (For example, it is only "bad" to engage in homosexual acts if one commits them out of self-ignorance -- perhaps, in order to fit-in with a crowd. But the same homosexual act can be "good" if it is committed out of self-knowledge -- perhaps, it is what makes one happy and complete. But homosexual acts themselves are neither good nor bad.)
(e) Just an additional point, it's easy to think that whenever bad things happen to us, we think that the other person deliberately intended to harm us. But there is a difference between intending bad things to happen to someone, and bad things happening to someone by accident. Extensionally, the "bad-event" (ie, the "injury") is the same in either case; there is no getting around the fact of a some things simply being "bad" for us. However, there is an intensional difference depending on what the intention (ie, "will") was -- and I want to say that this distinguishes between cases of "harm" vs. mere "injury." [Perhaps this is the difference between criminal and tort cases.] There is also a difference then, between "good-will" and accidental benefits.

Of course, there's a lot more to this than what I'm saying here, but basically, if you do things out of an intention to harm others, then you have a "good reason" (ie, a reason founded on a fact and no way to dispel doubt against it) to be paranoid and think that others might do the same to you. Furthermore, this "good reason" lies in the fact that the existence of a harmful intention is no longer merely a hypothesis once you yourself commit an act out of ill-will; it becomes an actuality, because there is at least one instance of ill-will existing -- your own. And since you have no "knowledge" (in a technical sense of the word) that yours is the only one, there is no way for you to erase the doubt that ill-will does in fact also exist in other people -- or, perhaps more importantly, that in your version of the world at least, the existence of ill-will is a proven fact. Since your version of the world is the only actual place where you live, it could be said that your world is "worse off" because ill-will and acts of ill-will truly does exist there. (On the upside, the same would hold true for acts of genuine good-will. Perhaps there's worlds in which both actually exist.)

In short, the point of the passage from Plato shows that if we are to have genuine "hope" (eg, perhaps a firm-belief that one "deserves" a good-ending, or a firm-belief that the world itself is ultimately good) that isn't simply based on the random chance that one gets lucky, then we would want some kind of indication that such things (eg, good-will) could, and perhaps sometimes actually do exist in some worlds. Even if we don't always have proof that they actually do exist in all worlds, we could still retain the belief that such things have the possibility of existing in some worlds, so long as we don't destroy the possibility altogether. This belief could be strengthened into something like "faith" (ie, a firm-belief) if we have proof of there being at least one true and actual case of the existence of good-will (not just situations that benefit us) -- but the only way that we can have such firm proof of there being at least one case of good-will is when it exists in our own world and when we are the actuators of that good-will. Such is the nature of things like "wills." It is not something that can be assessed by consequences, as Kant would say.

Now to bring it back to Kant: again, the phrase "of the aid he desires," is just there to give some actual content to the abstract notion of "hope." If it troubles you, just simply replace the phrase "of the aid he desires," with "of something good." But, perhaps the replacement might sound too vague or abstract to be useful and you'd prefer to go back to Kant's original language. If it doesn't sound too vague, then I think the replacement is fine. The point is that the focus should be on "hope" and not on the particular content of what the hope is about.

But why is this non-consequential? Because of the sort of thing that "hope" tends to desire by its definition (ie, hope always aims for "the good" -- even if "the good" is just simply for the good of the self or the good of one's own world), and because of the sort of thing that a "will" aims for by definition (ie, a "will" is quite simply a choice, and whatever it chooses is just what is called "good"). Without genuine hope that is grounded in something substantive, there could no "good reason" (ie, founded upon facts and not merely conjecture or chance) for thinking that "the good" truly does exist at all, and one could only rely on random chance events as being the cause of any beneficial events. And if there is no "the good," then that makes "choice" itself (ie, "will") totally meaningless. And thus, it is contradictory to live in such a world in which one wants to have choices, but in which "the good" truly does not exist. One cannot have genuine "hope" if there is no difference between choosing this or that. It would be a "Good-less" or "God-less" world, and it wouldn't make any sense.

I think that this is what Kant means.
And it is not consequentialist, despite what the cynical utilitarians like Hobbes think. Perhaps, they only say what they do because in their world, true-love doesn't exist. Or, perhaps they would say that if you believe in true-love without having loved yourself, then you are a fool; it takes one to know one. Still, even worlds -- worlds in which true-love has yet to show itself -- these need rules and guidance in order to stay safe in the meanwhile. Maybe that is what consequentialistic moral-theories are intended for -- to help those other worlds. In fact, perhaps it is these love-less worlds are the ones that are most in need of strong moral guidance.... (hmm, Jesus did say that he came for the sinners. Maybe it's kind of like that.)

Sorry it's so long. But I hope it helps.