Continuity mistake: Toward the end of the chat in front of the white house, in a far shot, Dr Floyd crosses his legs. The camera comes in for a close-up and he crosses his legs again. (00:11:52)
Continuity mistake: When Dr. Chandra enters his office he throws his keys onto a stack of papers on his desk. In subsequent shots, the keys are missing or appearing again. (00:13:45 - 00:15:20)
Continuity mistake: During the "aero-braking" maneuver the force dislodges a photo from Dr. Floyd's wall and stretches his face indicating many Gs. Similarly, the cockpit crew is thrown back into their seats, yet their flimsy microphone headsets are never dislodged from their heads. (00:35:22)
Continuity mistake: At one point when Chadra is repairing HAL, HAL starts speaking gibberish. When HAL starts doing this there are 8 blocks sticking out from the floor, but when Chandra stops HAL there are only 4 left. (00:55:15)
Continuity mistake: Dr. Chandra is in the logic circuits room reactivating HAL. He types words into a computer on the wall opposite the logic circuit panel (panel with the clear plexiglass blocks). In the movie 2001 there was no computer screen there; when Bowman is deactivating HAL you can see the flat metal wall with the red grid on the wall opposite the logic circuits. (00:55:50 - 01:34:05)
Continuity mistake: When doctors are discussing the medical condition of Dave Bowman's mother, a close-up of the African-American doctor shows a framed newspaper on the wall behind him. It is the front page and has prominent pictures of Bowman and Poole taken during their mission. In the next, wider shot, we see this wall suddenly has nothing on it - the newspaper and frame have vanished. They return when Bowman's mother sits up in bed. (01:16:45)
Continuity mistake: In "2001", the platforms that the pods sit on have a rotating circular surface that is grated with square holes, looking much like a gigantic satin-black waffle. In "2010" these discs are solid and gloss black - no grating whatsoever. (01:24:50)
Continuity mistake: In "2001", Bowman sneaks aboard Discovery through the emergency airlock. In the airlock's alcove is a spare spacesuit, green in color. He takes and uses the green helmet to cross the decompressed pod bay to access HAL's memory. After disabling HAL, Dave wore his red suit and helmet to leave Discovery for the last time, and would have had no reason to move the green suit before leaving, and no one else is aboard to have done so. In this film, we see the same alcove is entirely empty - the green suit has vanished. (01:41:50)
Continuity mistake: All the monitors aboard Discovery-1 are standard CRT screens of 1980s vintage (curved face), yet in "2001", they were all flat screens. and there's been no upgrading between the events of the two films.
Continuity mistake: Near the end, the Discovery's antenna is shown in a closed position (not pointing anywhere) before it moves, meaning prior to this scene, it could not have been used to communicate with the Leonov.
Answer: If they didn't, any further manoeuvring would require much more fuel. They would be moving the mass of two ships.