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.
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. (01:11:00)
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. (00:05:40)
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. (01:37:30)