I'm not talking about the nitpicks, like complaining about the accents of Elba and Rapace. Anything I offer here is purely from observing the movie, not listening to interviews or reading fan speculation.
Let's dig right in.
Needless to say, there will be spoilers.
(clicky the SPOILERS! for the rest)
1. Complaints that we don't know the "agenda" behind this mission.
Wrong. We know the agenda: old, desperate, likely-crazy rich man is spending his (or his company's) trillions of dollars because he hopes that our "creators" can renew his life.
So what that Vickers doesn't answer what the agenda of the financial backers happens to be when Holloway and Shaw are confronted by her. It is probably because her agenda (to prevent the mission from accomplishing much of anything) is counter to her father's agenda (get the creators to go all "fountain of youth" on his ass), which would probably be counter to the agenda the board of directors was given at WEYLAND.
2. Complaints about the team knowing nothing about each other or the mission until they came out of suspension.
God, I hope after point #1 that this becomes more obvious. Weyland couldn't tell WEYLAND that he was spending company money to keep him alive, could he? Weyland couldn't risk people bailing out before they got there and he couldn't risk a leak allowing someone else to charter a course sooner. Besides, the more people know the trip details before launch, the more improbable it becomes that this could serve as a prequel.
The biologist, when he found out what it was about, scoffed at the engineer theory. The geologist scoffed at giving any credence to cave paintings being an invitation or map for us to visit an alien race. Their reactions wouldn't have been uncommon.
3. The geologist and biologist were acting like scared high school students in a horror movie, when you'd think professionals that wouldn't fall apart under the circumstances would have been picked.
Again, details weren't revealed because they could not be revealed. More importantly, why were we going again? Because two scientists had a theory that we were created by an alien race and that race left an INVITATION for us to come find them. IF YOU BUY THE THEORY, you expect benevolence at your destination, at best, and desolation, at worst. You wouldn't be testing that these people can deal with the unexpected.
Mind you...the scene with face-hugger was a pure display of high school student in a horror film stupidity.
4. Where was the chain of command? Those guys would have been shot in the military for just saying they were going back to the ship!
This wasn't a military operation. Vickers wasn't being a cold military person, just a cold blooded bastard. The captain was just the ship captain. He didn't have complete command of everyone. You know why people didn't listen? Because they were all contractors that were in it for a paycheck.
5. How could they make this trip without any soldiers or someone to defend them?
The guy who got waved off with the whole "no weapons" thing? A merc, who those on the podcast misidentified as the geologist. The guys who were taken out by the infected geologist in the bay? Mercs. One of the guys who accompanied Weyland to the engineer? Merc.
6. Why is the android being such an evil dick or why is Weyland ordering him to be such an evil dick?
Weyland is desperate. Are the microbes that David found something that can change his "father" in some way that will renew his life? Will the life growing in Shaw be of some help to his agenda? Weyland spent a trillion dollars of money that isn't quite all his because he wants to live. He's on borrowed time in many ways, so he can't wait for tests to be run (if the biologist had even made it back), so it is on David to experiment and observe.
I get if you leaned over and asked someone during the movie, "I get that he has no soul, but why is David such a raging asshole?" But after? When the motivations should be much clearer?
7. The ship's captain says this ship doesn't have weapons...why would they send a ship all that way without weaponry?
I point you to #3 (peaceful mission to visit benevolent creators), #1 and #2 (the agenda of youth and purposely misleading many about it). You have a dying man with a trillion dollar Hail Mary to extend his life, banking on a theory two scientists have that (correctly?) flies in the face of known/established science. He bought in big time. If you approach beings so much further advanced than you THAT THEY CREATED YOU, do you A) want to risk offending them by going strapped or B) think you have a weapon that will lead you to be victorious over there? More importantly, if they turn out to not be benevolent higher beings that can save his life, he's already dead.
You have mercs because maybe you have to get past some stuff to get to a ruin or...maybe...because Weyland planned to leave no survivors that could spread the findings to others after he reaped his reward. But you don't ride a war machine to your tea time with "gods".
8. Complaints that Guy Pearce was used to play an old man, rather than just an old man
If this absolutely needs to have been a necessity...there's Scott's desire to do all the viral stuff. The Weyland appearance at TED TALK. He needed someone younger because it is easier to make a younger man look older than an older man look younger.
9. They had all this great technology, but it is a writing mistake for them to just accept that it might be glitchy.
Really? You think that, in the future, there won't be glitchy tech? Even when it is being deployed on a planet it couldn't have been designed for? We've had the automobile for a hundred years now and haven't quite perfected it to where we have no lemons. But I suppose you're expecting a fully functioning hoverboard within three years, because Back to the Future told you so, too, huh?
I'm not even someone who was thrilled by the movie. The wife, who was mostly going because I wanted to, enjoyed it more than I did. But entertained me and it doesn't deserve so much of the illegitimate criticism it gets because some wanted to be spoon fed, some wanted it to link up to the Alien/Aliens movies as much as they expected (but weren't told it would be) or have more action (which the trailer might have led them to believe).
Edit: Oh and just in case it came across the wrong way: I love the folks over at Comedy Film Nerds. Phenomenal podcast and reviews with humor liberally scattered throughout. I probably wanted to hurt my iPod so much because I love those guys and couldn't understand how "they just didn't get it!" ;)