It's hard to choose, there are so many. Obviously most people point to the classic "running in a straight line" scene, and I can't deny it's an iconic moment, but being a bit of a hipster, I prefer the subtler, less blockbusting moments of stupidity. The ones that reward repeat viewings, reassuring the viewer again and again that "yes, it really was that stupid."
Things like the casual dismissal of evolution for humans but not animals even though we share DNA, because a scientist "chooses" not to believe it. Or the idea that we share 100% of our DNA with our creators, when that would just make them human and there'd be no need for some elaborate creation ceremony. Or that time a biologist runs away from the first discovery of a dead alien body, but then tries to cuddle a live evil slimey vagina snake. Or the bit where the geologist with the automated mapping devices whose still in constant contact with the ship, manages to get lost. Or the bit where they all take their helmets off. And then the bits where they all continue to do so on every mission, even after one of them gets severely sick and has to be unnecessarily burned alive in front of his lover after showing symptoms for all of 5 minutes, when as far as anyone knows he got sick from taking his helmet off. Or that bit where Idris Elba goes and has sex while members of his crew are still missing. Or that bit where he decides to scan the atmosphere as they're descending onto the planet (good thing it wasn't a gas planet, ey Cpt. Dickhead?) Or that bit where he turns up in a wetsuit to explain the plot because the writers suddenly realised no one has any clue whats going on yet. Or that bit where he commits suicide just 'cos Shaw tells him to. Or that bit where they all let Shaw come on the final expedition with them immediately after giving birth to an Alien, even though they've just burned a guy for looking a bit peaky and two of the very people on that jaunt had literally just quarantined her. Or that bit where Guy Pierce turns up in Doctor Who make up and no-one cares. Or that bit where David is learning all those languages manually like a human when he could surely just be programmed? Or that bit where he activates the alien ship by pushing some soft boiled eggs and blowing into a recorder even though he has no breath. Or that bit where the head from Art Attack has an orgasm and then explodes. Or how almost all the cast are speaking in accents even though there's no need for it, and Noomi Repace really, really can't do it. Or how Charlize Theron is implied to be a villainous character entirely by dressing her in an evil computer game bodysuit, even though she's probably the most sensible person on the entire ship and does virtually nothing of either harm or use the entire time. Or that bit where the Undercover Boss turns out to be her father and it makes no difference to anything or anyone. Or that bit where a zombie shows up for absolutely no reason and attacks and kills a bunch of crew members we've never seen before. Or how he's folded up like an Scorpian when he does so because...something? Or how Holloway is such a massive sulky cock biscuit he gets drunk at the disappointment of only discovering the first example of alien life, after a mere 6 hours of exploring one tiny part of a huge planet. Or that bit where the Engineer decides to come back and fight a small, injured woman rather than just getting into another ship. Or how the legend of Prometheus doesn't actually relate to the plot of the film in anyway whatsoever.
All of that is good, admittedly. But when I really think about it, I'd probably have to go with the bit where the hologram of the supposedly long dead Guy Pierce looks at the real life human actors he's not supposed to be interacting with.
I love that Movie. Not sure why after reading your review, but I still love it. W/e 
It'd be like the makers of The Shining, laughing at the theories presented in Room 237. 