Factual error: During the drag racing part of the film, they show an orange Plymouth lining up to race a red 57 Chevy. When the back of the Plymouth comes into view you can see a Direct Connection license plate with a Mopar logo on it. Chrysler's Direct connection line didn't exist in 1964, and the red white and blue Mopar logo wasn't around until 1972.
Factual error: Throughout the film the British infantry are armed with carbines. These were intended for issue to cavalry and are much shorter than the infantry issue Martini-Henry rifle.
Factual error: The lid Halloran removes before the jump out of the plane is much too small. They wouldn't have made it through the opening with their parachutes strapped on. (01:05:45)
Factual error: Captain Willard recalls back to lunch at General Corman's and we hear Harrison Ford's voice say as he points to a map, "Now he's crossed into Cambodia". The town he's pointing at (Ban Me Thout) and the one above it are in the Central Highlands in the middle of Vietnam and not crossover points anywhere near Cambodia. (01:18:20)
Factual error: When John Belushi, Wendy-Jo Sperber and Treat Williams are on the stolen motorcycle, Belushi gets mad, pulls a pin, and disconnects the sidecar from the motorcycle. This is not how sidecars are actually attached or they wouldn't go the same direction as the bike.
Factual error: When they visit "Ireland", presumably the Irish Air Corps aerodrome in Dublin at the time of WWII, all of the staff in the bar at the aerodrome are American servicemen, in neutral Ireland.