"There's one known nitpick that can be explained away; the rest is pretty darned solid."
I agree it's extremely solid and well-thought out, but I think there's more than "one known nitpick" (though all the nitpicks are pretty minor, and probably more due to constraints on what they could do with their effects/budget than to their scientific consultants missing things). Aside from the thing Tyson mentioned about the liquid in the straw, I've also seen it mentioned that the moondust billows like it would in an atmosphere when Dr. Floyd's ship land on Clavius, along with the following issue about the size of the Discovery's centrifuge mentioned in the awesome book (for 2001 nerds) 2001: The Lost Science:
We had the option of putting the Centrifugue on for, say, one to two hours a day to produce up to 1.5 g, or permanently have it rotate to provide about 0.2 to 0.3 g. We chose the latter. There was, of course, the problem of Coriolis forces, which on small diameter wheels would cause dizziness to astronauts walking along the rim. Calculations showed that a centrifuge should be at least 300 ft in diameter to reduce to acceptable levels the inconveniences caused by the Coriolis forces, but such a diameter was beyond the capabilities of the M-G-M British Studios - and our budget. So we never really mentioned the diameter of the wheel with which we had to work; in fact, there was no purpose to reveal the measurements at any time. Visual appearances were what counted.
Another one that occurred to me recently watching the movie: why is it that in the scene with the meeting inside the Clavius base, they seem to be walking around in normal Earth gravity, not hopping around in moon gravity? I suppose you could always say that the moonbase has an internal centrifuge where the meeting took place, with floors slanted at just the right angle so that the sum of the gravity vector and the "centrifugal force" vector is perpendicular to the floor, and with the size of the summed vector being equal to that of Earth-gravity. The external shots of the base don't show anything that looks like a rotating ring but it could be buried underground.
Finally, while HAL was a pretty good depiction of what 1960s A.I. researchers might have imagined an advanced A.I. to be like, in retrospect the way the 9000 series has had a "perfect operational record" up until his catastrophic breakdown doesn't seem like it matches how modern an A.I. capable of fluid human conversation would be likely to work--it'd likely be an adaptive system more like a neural net, one which is expected to make frequent errors when dealing with new problems (including new conversational situations) just like a human would. The 9000's perfection sort of implies they were some sort of symbolic A.I. (the approach that was popular in the 60s), like an expert system pre-loaded with high-level concepts and decision-making rules.