Revealing mistake: Towards the end of the movie when Burnett is by the plane's ejection seat, you see a puddle of water by him with snow flakes floating on top of the water. Snow flakes dissolve in water as soon as they hit. They use a corn starch type mixture to make fake snow, and that is what you are seeing in this scene.
Plot hole: When Burnett is hiding in the mass grave, the people on the ship are watching a thermal image of him. When he falls, his arm is at an angle and stays at that angle. To move under the bodies in the grave he would had to have moved his arm. But it stays at the same angle throughout, so how could he move under the bodies, without his thermal image moving? (00:42:00)
Revealing mistake: When Owen Wilson is trying to restart the beacon in his ejection seat, his right hand is ungloved. Yet in the scene before, he took off his left glove. It is my belief the negative is reversed, as you can catch a quick view of a Duracell battery with the letters mirrored. (01:24:43)
Other mistake: At the very end, in the helicopter, Gene Hackman is wearing a full helmet with a mouthpiece so he could hear and talk to the people in the helicopter and back at the ship; Owen Wilson is not wearing a helmet or a mouthpiece. There is no way Owen Wilson could hear what Gene Hackman is saying and vice versa. Battle helicopters are very noisy; you must have a helmet to hear and a mouthpiece in order to speak to be heard.
Other mistake: When they show the Super Hornet ready to take off on the carrier we see lots of people standing around watching on the deck. The people are there because it is file footage of the aircraft's first carrier trials on the USS Harry S. Truman in 1998. As they bothered to CG paint over the trial markings on the plane, they could have erased the people at the same time.
Factual error: The heat seeking missiles would not have gone after the fire ball created by the fuel tanks as shown in the movie. Heat seeking missiles don't go after just any heat. They go after specific frequencies of infrared found in jet engines.