For me the biggest problem was people not doing their jobs.
In Alien the mechanics repair the ship, the navigator plots the ship's course and calculates the distance from Earth, the Science Officer does science. This helps us identify them and gives their character some flavour.
Parker and Brett are vital to the running of the ship but are paid less and this creates friction.
In this film we see a little bit of the medical officer doing medicine and it seems that the bridge crew steer the ship but that's about it.
If the script had been arranged around what the characters did it would have made more narrative and dramatic sense.
The biologist should have been fascinated in the dead aliens and wary of the living ones.
He should have been obsessing over the decapitated head and Shaw (the archaeologist) should have obsessed over the carved one (which she almost fails to notice in the current film).
She too should have had some grasp of the latest interpretation of the same Vedic languages (maybe not as fast or as detailed) that David has studied.
She should ask David for confirmation and maybe be wary of some of the spin he seems to be giving his readings (creating friction).
If Fifield had been the Cartographer, he could have been keen to map the other buildings and get trapped in one of those because the storm interferes with his instruments.
If the bridge crew had been closely monitoring what was happening to the stranded guys via their headsets (instead of sleeping with the boss or just sleeping) we would have had a more tense scene with the crew powerless to help them. The sound of what was happening to them being the main source of information would make the few bits we see more intense (think the air duct scene in Alien).
As I suggested earlier the crew could be more defined if there were less of them doing more.
Making Holloway the biologist makes more sense than having him the 'other' archaeologist who does even less archaeology than the main one.
Making the nurse the android and having her played by Theron makes sense and condenses three characters into one rich character that is narratively stronger.
Making Kate Dickie Vickers gives the film three strong females which are significantly different in look and role.
Having the crew know where they are going and what they are doing before they go to sleep makes them seem less stupid.