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?
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.
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.
Factual error: When the CIA guys are 'invited' to the secret underground base via the highspeed drop platform - shouldn't they be flying off at the speed the platform is descending?
Revealing mistake: When Millbarge changes the missile's programming at the last instant, the rocket changes course simply by rotating the shooting frame - and even if it could change course like that, the angle of ascension would be wider than indicated on the bunker base's computer screen.
Continuity mistake: When Milbarge and Fitzhume are driving the ambulance and are being chased by the Afghans, one on horseback rides up to the driver's side and tries to smash the door window. First the window is down, then Milbarge rolls it all the way up, and just before it is shattered with the butt of the AK-47, the window is about a 1/4 way down.
Continuity mistake: When Dan Aykroyd and Chevy Chase are first impersonating the two doctors and in the tent, the other female doctor (not the blond one) never leaves the tent with the rest of the doctors. She just disappears after she is introduced, and comes back when they are in the operating room tent.
Factual error: This is more of an understandable error: In the movie, the Russians still use the AK-47 or the AKM; at this time, the Soviets had the AK-74, a small caliber version of the original AK with plastic magazines and a large but effective muzzle break. At that time, AK-74s were hard to come by for the American movie industry, though.
Factual error: Fitz-Hume and Millbarge shoot the rocket base crew with tranquilizer dart pistols. But the crew wear thick winter clothing, and air-powered darts should have trouble penetrating deep enough to deliver their load - and the serum would not take effect immediately for that matter (the guards drop as soon as they are hit).
Continuity mistake: When Dan Aykroyd and Chevy Chase are getting ready to take the FSB Exam, the test monitor angrily puts a test booklet on Dan Aykroyd's desk, then immediately returns to the front of the room without ever putting a test on Chevy Chase's desk. In the next shot, Chevy has a test on his desk.
Deliberate mistake: When the Russian tosses a grenade toward the wood pile when Fitz-Hume and Millbarge are, Fitz-Hume catches it. Trouble is, he is looking up, as if expecting it, when anyone else would be hunkered down. Then when he tosses the grenade back, it's in a manner that would give it a high arc. Instead, it flies straight into the window of the building.
Continuity mistake: As the rebels are chasing the ambulance, you see one with a yellow turban come up to the back end and jump on. He apparently missed and was left rolling in the dust. If you look at the edge of the truck, you see the yellow turbaned head poking up, but another guy rolling in the dust. There was only one guy on the horse.
Continuity mistake: When the duo are sent out for their training, they are sent parachuting. The sky lightens and darkens between shots. In the close ups, the sky is black. In the wide shots it's blue.