When the man with the feather in his hat takes Blankes and Copeland's guns during the riot, their names are clearly printed on the butt of the guns. However, when he raises one of the guns to put it in Lt. Harris' face, there is nothing printed on the butt.
During the talk between Mahoney and Captain Reed in the interrogation room, in one shot the patches on Mahoney's shirt switch sides and are mirrored (indicating a flipped shot) and after that disappear completely.
As the giant camera booth hits the water, the top black panel falls off, but is in place again for the next shot.
During Leslie Barbara's final confrontation with the Teskey gang, Leslie is holding the baton handle in his hand for most of the fight. The handle then switches around between shots, as it is hooked around the neck of the gang leader, without Barbara seen flipping it.
When the girls are following George Martín by the fire at the beach party, the third girl in line appears again as the sixth girl in line, although in the later shot she appears with more clothing than in the earlier shot. This is because the scene is cut up into several shots in editing and shown in the wrong order. The second shot featuring this girl is the beginning and the first shot is the end of the same take.
When the cadets are en route to the riot, it shows Harris getting orders from Lassard on where to deploy the cadets. In reality for situations like the riot, there's a whole incident command system that would be in place. This involves operations officer giving orders from the over all Incident Commander. Harris would have been getting orders from the operations officer to where to go not Lassard.
When Captain Reed and Mahoney are in the interrogation room at the police station, Captain Reed tells Mahoney that the duration of the police academy is 14 weeks long. When Mahoney is at the academy Commandant Lassard tells him the academy training is 24 weeks long. However, Lassard gets the length of time wrong repeatedly throughout the film, even having to be reminded of it when inspecting the new cadets.
When Captain Harris tells the cadets that Blankes and Copeland will be the cadets in charge, he says ¨Blankes and Dopeland.¨ This is probably deliberate as Captain Harris doesn't respect Copeland as much as Blankes, as indicated by Harris's reaction to Copeland attempting to shake Harris's hand earlier.
When Hooks makes it over the top of the brick wall you can see a seam showing it is not a real wall but a prop. It also bounces a few times whenever someone climbs it.
After Hightower flips the police cruiser over, we can see that there is no engine in the car when Lt. Harris is reprimanding him.
The police car used in the obstacle course scene is a 1978 AMC Matador but the car Hightower flips changes to a 1974 model, which has a divided grill and round turn signals. Later model Matadors have a continuous grill with rectangular turn signals. The car also has no engine.
When Barbara hits Copeland with the tray in the cafeteria, the tray is already dented before it even hits him.
When Hightower is doing his driver training the driver's window is down on his car as he drives through the water shower. However, for the rest of the scene and when he emerges from the car he is bone dry.
When Captain Reed and Mahoney are in the interrogation room at the police station, Captain Reed says, "He was a good friend", meaning Mahoney's father. When he says it, his lips don't match to the words he's saying. The original line spoken was "He was a good cop".
When Tackleberry is playing the saxophone at the beach party, his fingers do not move. It is obvious that the sax playing is recorded. However, during the shoot David Graf was playing the saxophone as he was a skilled player. Likely the music simply wasn't synchronized correctly.
Crew and equipment is reflected in the trainees helmets during the riot.
During the scene where Hightower (Bubba Smith) flips the police car in training (at the 1 hour 10 minute mark) as the camera pans down to the ground, off to the far right, for a brief second you can see a large bare arm of what appears to be a crew member (hidden behind the car) that aided in flipping over the car.
Reflected in the TV that Cadet Martín carries.
When Mahoney is teaching Hightower how to drive, the sign on the storefront is spelled Chiropractic "Centre" indicating a Canadian location.
After the fight between Blankes and Mahoney, they are taken to Harris' office for reprimand. After Mahoney falsely admits he was the one who threw the first punch, Harris throws Mahoney out of the academy. This goes against Lassard's request from Capt. Reed to keep him in the full 14 weeks and Harris had already stated to Mahoney getting thrown out was impossible.
When Mahoney goes to give his speech, you see the hooker whom Blake and Copeland brought to Barbara's room to get him in trouble, ended up hiding in the podium with Mahoney and giving Lassard oral pleasure while he is speaking. It is never explained how Lassard finds out about the hooker since he never had seen her before, and didn't know she was one in the podium with Mahoney.
Since they are not sworn officers, police academy cadets cannot engage in any form of law enforcement, therefore putting them in riot gear with the expectation of controlling a crowd, or just any form of law enforcement, would be legally null and void afterwards.