Continuity mistake: Pvt. Pyle is on the rifle range with Gunnery Sergeant Hartman right behind him. When filmed from Pyle's right side, he is wearing a white wrist wrap/brace but the shot moves behind him and it is gone. Back to the right side and it reappears. (00:35:50)
Continuity mistake: When Gomer Pyle is in the toilet with his rifle and after shooting the drill instructor, Pyle sits down on the fourth toilet seat from the back of the room. In the next shot where Pyle kills himself, he is sitting on the third toilet seat. You can see this already from the front shot of Pyle when he kills himself because there is a rise in the wall next to the third seat, which is visible through the whole scene. It is more obvious in the following shot where you can see the row of toilet seats and Pyle sitting dead on the third one. (00:43:00 - 00:43:35)
Visible crew/equipment: When Cowboy, Joker, Rafterman and the other Marines are running across the buildings to get to Animal in the final sniper scene, watch the foreground. Right before they reach Animal, you can see they run by a crouching crew member, in the foreground at the bottom of the screen. (01:38:52)
Revealing mistake: When the Marines are jogging through the training camp complex, singing "I don't know but I've been told..." you can see the British road junction markings on the tarmac underneath them. There is little evidence to suggest that there was any attempt to disguise or remove them.
Continuity mistake: During the drill scene when Sgt. Hartman is asking Private Pyle if he knows the difference between his left and his right, watch the positioning of Pvt Pyle's cap. After being struck the first time, the cap is slightly cocked. After the shot returns to Pyle and before he gets struck for the second time, the cap is cocked further over. (00:09:14)
Continuity mistake: During the "blanket party" scene, Pyle appears to be sleeping on two (wrinkled) pillows. When Cowboy covers his mouth Pyle is sleeping on one very neat pillow. (00:28:39)
Continuity mistake: In the bathroom scene on the last night of boot camp, Pvt. Pyle is 'training' with a rifle. As he snaps to attention, the shot from behind shows him with legs slightly apart, a second later the shot from the front shows him with his legs perfectly together, yet he never moves.
Continuity mistake: During the graduation parade, if you look at the background you can see many large squad bay buildings with a few single trees in front of them, this scene seems to be shot at the actual Paris island. However when they show a close up of Joker's platoon in parade, the background changes to mostly trees, with only two or three small buildings behind them.
Continuity mistake: When the tanks are moving into the city with the Marines i.e. after meeting Private Cowboy, Animal Mother and the rest, they run into a firefight. When they stop shooting and are reloading watch the leader's ammo clip. It's missing in one shot of him, in the next he's ejecting the magazine and putting in a fresh one before shooting the two Vietnamese with it.
Continuity mistake: When Joker and Rafterman are in transit on the chopper, we see the gunner firing out the cargo door. We can see out the cargo door that the ground is pretty far away, the chopper is obviously pretty high up in the air, so high that if there were people down on the ground it would be rather hard to see them. However the camera switches to the gunner's point of view shooting at people, and the chopper only seems to be about 20 feet off the ground.
Revealing mistake: When Private Pyle shoots himself you can see that the blood splatters from the side of the screen instead of going straight back from the back of his head.
Chosen answer: A Drill Instructor is always mad at the recruits in order to forge discipline. Private Pyle was the biggest screwup in the unit, thus creating more work for him.
Captain Defenestrator