We're past 2001....2101 is not as impressive in 2007 as 2001 was in 1998....Maybe use a figure like the name of a Messier object or an exoplanet....

The Sun is as big as the Moon from Earth..when shown, no star can be visible around it! If we use the same overture sequence, be sure to show the exact lunar landscape where it is shown.

Shorten the prehistoric chapter...many animals are not that necessary to the plot.

When the bone becomes the space platform, use morphing techniques.

The stars are well known. Softwares show what star is where and when at its magnitude and color. Stars don't move and cannot be shown near a sunlit object. Moon and Earth phases must be respected (not the case in the movie).

Forget the velcro, take advantage of the amazing weightlessness...Hatches are not doors...80 cm wide hatches are enough and a lot safer. Rotating space station? Only if the structure is very large otherwise hello space sickness!

The Moon has very smooth mountains, no peaks, cliffs.
A space shuttle with only one passenger? Impossible!! Suits for space faring humans needed (no shirt, tie, jacket but an overall with lots of pockets and velcro tapes).
A moonbase like Clavius: not likely...Every space would be functionnal, no wasted space. The conference on the Moon would happen on Earth.
The Moonbus trip would be done on wheels (much safer).

No haze in front of the lamps lighting the monolith...Spacesuit with a golden visor (adding mystery to the faceless astronaut, reflecting the landscape on his helmet). When the radio beam is emitted, they should turn their radio off (chestpack), not put their gloved hands at their helmet, at the level of the ears...

Discovery 1 lacks radiators (making it look like a bird); the front module can have any shape, why spherical? No need for pods if no landing is planned. The centrifuge is far too small to be usefull (Coryolis effect).
There should be 3 or 5 computers, not just one (democracy). If AI is really advanced, humans won't be justified....Making it hard for the plot.
Hibernation? Hmm, perhaps...

Space scenes must indeed be silent...and silence can be filled by (classical) music: Good point for 2001.
The stargate: shouldn't the trip be instantaneous? No need for all those special effects.

There are obvously many other ways to perfect te movie!