Plot hole: When Fitz-Hume and Millbarge disguise themselves as aliens in order to distract the mobile launcher crew, where exactly did they get the foil they are wearing? Except for the satellite dish Millbarge wears on his head, no parts of their code transmitter can have been used or the thing would be of no further use, and it is very unlikely that either of the two spy groups brought any of the foil along.
Continuity mistake: After the grenade sets off the box of grenades, and the subsequent explosions demolish the building, Millbarge says "I'll get the horse." Trouble is, throughout all of the gunfire and the explosions, there is no sign of the horse; it would have run off somewhere. When he gets the horse, it's tied up right next to the now demolished building. It would have been killed by the gunfire and/or the explosions.
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Other mistake: When Chevy chase is being filmed cheating on the exam, all the video cameras are on the sidewalls near the roof. But later when they view the footage, the last shot of Chevy copying the answers is from the floor level where no camera was seen in any previous shots. Also what was a floor level camera going to film anyway...everyone's feet?
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