I would say the biggest criticism, or most recurring, regards the behaviour of the characters. I think it really boils down to them not behaving as expected or more specifically as professionals.
Fiction allows us to fashion something of an idealized version of reality, one where we can accept characters that are larger than life or at least certainly better than our real experience. Indeed we almost always expect that from fictional characters. They're often expected to reflect more of who we'd like to be rather than what we're really like. This is certainly true in shows and films depicting cops and lawyers. Cop and lawyers stories rarely depict these worlds in a very realistic way. In the real world there's a lot of mundanity and routine that at best is only hinted at in film and television. For the longest time Westerns painted a very idealized portrait of the Old West and the people who inhabited it. It wasn't until the '60s that we started to get films that began showing the grit and shades of grey of that time. Now we applaud films that shows us more of the reality, but at one time it could be jarring for some audiences.
In the real world it's not uncommon for us to question the choices made by governments and business and organizations particularly in regard to seemingly unsuitable individuals posted to positions of great responsibility. I'd say it happens often that people who should know better still make bad choices and do stupid things.
When I look at the crew of the Prometheus I find myself thinking, "Who chose these losers? By what standards were they judged by? What idiot is running this operation?"
At the core of this, of course, is Peter Weyland's agenda for the mission. He was willing to invest a trillion dollars to what end? He wanted advanced science and technology to prolong his own life. There was no real nobility or ideal in his pursuit. Granted if he'd found what he'd wanted it could have had a spillover effect for others back on Earth, but that wasn't his conscious intent. He was focused solely on prolonging his own existence.
The inclusion of Shaw and Holloway gave the expedition a veneer of idealism or nobility of intent: the expedition was to (hopefully) make contact with extraterrestrial intelligence and possibly explore the origins of human life on Earth. That really sounds like a genuine Star Trek story. But Weyland Industries isn't Starfleet and its goal is not simply to seek out new life and new civilizations.
And so beyond Shaw and Holloway (who may be decent scientists in their own right though not necessarily suited for such an expedition) why were the other individuals included? None of them looked like the kind of individuals you would really want on such an expedition. Perhaps they were yet again just a way to give the expedition a veneer of noble purpose? Perhaps it didn't matter they were total screw-ups as scientists (and indeed they were)? The same could be said of the choice of Janek and his crew. Janek and his crew were simply meant to be truck drivers and with no expectations beyond that.
Who is at fault for why practically everyone dies in this story? I'd say it was Peter Weyland because he was blind to everything else beyond his not wanting to die. He initiated a situation that put completely unsuitable people into a place they had no business being. After spending a trillion dollars for such a monumental venture he went cheap on the hired help. Now that likely wouldn't happen in a Star Trek like story, but it has been known to happen in the real world. And films like Alien and Prometheus are supposedly the SF equivalents of films like The Good, The Bad And The Ugly, Pale Rider, True Grit, Dances With Wolves, Unforgiven, 3:10 To Yuma and Appaloosa. Perhaps a closer equivalent would be a film like Outland from 1981 with Sean Connery, the SF equivalent of High Noon.
Now what I posited above is how I could interpret what I saw in the film. That said I hope they use a different writer for the sequel. And hopefully the sequel will address some of the questions in Prometheus: what did things happen the way they did? Perhaps some of those answers might also be in the deleted scenes to be included in the disc release later this year.