Factual error: When the Marines are in Vietnam, most of them have the M-69 flak jacket. This body armor was first issued in 1969, while the rest of the film takes place in early 1968. In addition, the vest would've been largely issued to the Army, not the Marines. Their vest would've been the M-55, which is different in shape and design.
Continuity mistake: Just before the jelly doughnut scene, as Hartman is walking up the aisle, he is in front of Joker's locker, about to reach Pyle's locker. A moment later he comes to Joker's locker, before he gets to Pyle's.
Factual error: The flashlight that Pvt. Joker is using on his last night of basic training is a "Mag Light" that wasn't invented until approx. 6 years later. And the "yield" traffic sign the platoon is jogging past is of the style that didn't come into existence until approx. 1973-74, (i.e. red and white). In the 1960's the sign would have been yellow with black letters.
Character mistake: When Sgt Hartman is giving the lesson about Charles Whitman, he says that he killed 12 people - in reality he killed 17.
Other mistake: In the first PT run if you look at their boots you see they have their trousers bloused, this doesn't happen in boot camp till week 3 or 4. In the next scene they are at drill and no bloused trousers.
Continuity mistake: When Hartman slaps Joker, Joker's head is turned sideways by the slap. A moment later, he is looking straight down.
Continuity mistake: During the scene where the Joker moves into the building to kill the sniper, the sniper sees him and starts shooting at the pillar he is behind. During this shot, large chunks of the pillar fall away, but in the next shot, when the sniper gets shot, the pillar is intact.