Corrected entry: When Dave Bowman blows the explosive bolts on the pod to get into the Discovery, he flies into the long airlock, then back out towards the exit. Watch the pod through both of these shots; it doesn't move a single centimeter when the bolts explode and is in the exact same position when Bowman's body heads back towards the exit. Even with the best possible maneuvering thrusters automatically set to hold the pod in place, it would have moved significantly when the explosive bolts were set off. One corrector proposed that the pod would be held in place because the mechanical arms used to open the airlock would have held it there. Incorrect; Bowman released the pod's grip on the discovery in order to turn it around. The same corrector proposed that the expolsion would not overcome the forward inertia of the Discovery. Wrong again, the pod and Discovery are traveling at the same speed; an explosive decompression would push the pod forward at great velocity.
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Correction: Not so. The pod would be weightless in outer space but it still has mass and inertia. The total change in momentum of Bowman and the air escaping from the pod, applied to a pod with about the mass of medium sized car, would result in the pod moving away at only about 50cm per second. That would be barely noticeable from our point of view, even if the change wasn't immediately corrected by an auto-pilot mechanism, which is feasible. We can calculate the reaction speed of the pod this way : assume a gas volume of 4 cubic metres, a mass for the pod of 2500 kg, a mass for Bowman of 150 kg, an average delta v of 100 m/s for the air in the pod, and a delta v of 10 m/s for Bowman - all of which yields a result of 0.5 m/s, and if air pressure in the pod were lower it would have moved even more slowly.