Continuity mistake: When Harold Ramis is fighting Bill Murray to try to keep him from leaving the base, notice when Harold is on top of Bill choking him, there is a duffel bag under Bill's head, and in the cut-aways the bag is a few feet away.
Continuity mistake: When Bill Murray's girlfriend is leaving him for good, she puts her left boot on twice.
Continuity mistake: When Harold Ramis pays off his pushup bet with Bill Murray, he throws the dollar bills onto Bill Murray's chest, and they move around and their number changes.
Continuity mistake: When Harold Ramis is fighting Bill Murray to try to keep him from leaving the base, Murray's knit cap moves on and off his head during the scene.
Revealing mistake: When Bill Murray is blowing up the prison door, you see the explosion, but the explosive is still intact.
Factual error: Even in the '80s obesity was a strict disqualification for military service. John Candy wouldn't have had a chance of passing the required medical.
Continuity mistake: During the mud wrestling scene, a patch of mud alternately appears and disappears on the stomach of the woman in the white bikini.
Factual error: Then, as now, every recruit reporting to boot camp would be tested for illegal drugs, first by a urine test and then by a broad spectrum blood test in the case of a positive result. There is no reason for Elmo to try to hide his stash when the recruits are told they are to be tested - he is going to come up positive anyway. He may as well just say he has changed his mind and walk away. He is entitled to do that any time up to ten days after he signed on, and it happened a lot in real life!
Continuity mistake: When the platoon is escaping in the EM50, Sarge is on top and says, "I'm getting too old for this #%&*," he then lowers his head. The next shot, he lowers it again.
Continuity mistake: During the graduation scene, after the platoon arrives in front of the General's stand, Bill Murray begins running backwards. The shot changes to the girls in the stands laughing, and then back to the platoon. When it gets back to the platoon, you can see that Murray is once again just starting to run backwards.
Factual error: When the men are practicing for graduation they are using M1 rifles. The army had already switched to the M16 long before the 80s.
Continuity mistake: During the graduation scene, watch the band director closely when the music stops - you will see that his arms are still moving, as if he's conducting the band.
Continuity mistake: When John drives the woman over the bridge in the cab, just before he stops the car there is a shot of the two occupants and behind the cab the bridge is deserted save for one red van. When the shot changes to an overhead and John stops the cab, the bridge behind them is crowded with traffic and the van is gone.
Factual error: The Czechoslovakian Border Guards are armed with what appears to be an Uzi submachine gun fitted with a stock. Soviet Bloc countries didn't use foreign firearms. The guards would have had Vz 58's which are visually identical to AK-47's.
Continuity mistake: When they are escaping from the prison camp, they knock over grungy, drab green 55 gal drums, which are nice and shiny inside.