Factual error: When 8-ball gets shot, in the shot which shows the platoon ducking near a wall with Cowboy, Joker and Animal Mother in the front, there are two weapon related errors. Cowboy's M-16 has a nickel (silver colored) firing assembly and Joker's M-16 has an A2 type pistol grip. The A2 types were introduced somewhere around the 80s, and nickel plated assemblies are rarely used (and were invented after Vietnam, too). The nickel assembly is visible at the beginning of the shot, and you can see the A2 grip when Joker is changing magazines (while Cowboy shouts cease fire).
Factual error: When Pvt. Pyle commits suicide, he shoots himself through the skull at point-blank range with the tile wall of the bathroom only inches from the back of his head. The wall becomes splattered with blood and brain tissue but no hole in the wall is visible. Both the shot through Hartmann and the one through Pyle would have punched through the bathroom walls and quite possibly caused injury or death to anyone on the other side.
Factual error: In 1968 the USMC were still using the Sikorsky UH34/S58 helicopter (powered by a piston engine) but the helicopter seen in the film is the British version of the same aircraft, the Westland Wessex - gas turbine powered, it has a quite different nose shape from the original American version.
Factual error: At one point Joker is doing chin ups, with Hartman motivating him. Joker does three chin-ups, but not a single one of them was done properly. You're supposed to lock your elbows all the way out on the way down, and your chin needs to clear the plane of the bar. Joker never locks his arms out, barely gets over the bar. In reality Hartman would have been all over him about this, drill instructors are notoriously strict about proper technique.
Factual error: In the sniper scene where Animal Mother disobeys Cowboy to go help 8-Ball and Doc, and Animal Mother peeks around the corner of a building to try and see the sniper and the sniper shoots at him, narrowly missing his face, the impact of the sniper's bullet on the wall and the sound of the gunshot occur a split second before the muzzle-flash in the distant window from where the sniper is shooting from. This would imply that both bullet and sound have travelled faster than light.