Other mistake: As the ground team are on their way to the mars base camp, Carrie-Anne Moss' character is also searching for the base camp via a fixed camera on MARS-1. As the camera finds the destroyed camp, the view switches between various angles/viewpoints from around the camp. These views would be impossible to take from the camera(s) on MARS-1.
Other mistake: At the ending climax as Bowman is cutting the oxygen pack from Gallagher, you can see Gallagher's name plate on the front. However as Gallagher was running we clearly saw him take off his own pack, toss it aside and put on Burchenal's. This is made blatantly obvious as the camera pans to the discarded pack on the ground with the name "GALLAGHER" printed on the front. Which means the nameplate Bowman removes should read Burchenal, not Gallagher. (01:39:25)