For me, it's a tossup between the scene in Wing Commander where a damaged fighter is pushed off the deck (with the pilot still in it for added drama)... where it promptly drops. They're in deep space, and the stupid thing behaves as though it's near a planet. Facepalm number 1.
The second and third are from Armageddon, firstly where it's stated that the incoming asteroid will kill everything on Earth, "down to bacteria". I was suspicious enough to use the numbers given (97 billion tons at 36,000 miles per hour) to work out how much energy would be released by the impact... and got the result of 3 million megatons. That would be bad, yes, but the Dinosaur Killer yielded an estimated 100 million megatons, and there were survivors. The second example from Armageddon was where we, the audience, were expected to believe that one nuclear device would be able to split the asteroid cleanly (mostly) in two, instead of fragmenting it. Riiiiiight...