(at around 8 mins) 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".
(at around 46 mins) 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.
(at around 1h 29 mins) When Hightower punches the "Main Bad Guy" and knocks him through the door there is nothing tucked into his pants. When he lands at the bottom of the stairs, he has one of the revolvers tucked into his pants.
(at around 1h 22 mins) 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.
(at around 1h 24 mins) 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.
(at around 20 mins) Straight after getting buzzed, Blankes has no sideburns/level with top of ears and brutally/stupidly shaped behind the ears. When Lt. Harris compliments them on their haircuts, Blankes has sideburns and his neck fringe is quite a bit longer.
(at around 5 mins) When Mahoney is parking the Trans Am, there is a Nissan Stanza with license plate VLT 406 behind the car owner and manager. When they run to see what made all the noise, the Stanza has turned into a Buick. There also appear to be empty parking spots to both sides of the Stanza, so he didn't need to wreck the Trans Am. In the next bit where the photo booth is dumped over a bridge, the same Nissan Stanza crosses the bridge and stops to avoid hitting the men from the truck.
(at around 9 mins) 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.
The handgun range they're learning on is outdoors, with targets at 25 meters/yards. In reality trainee police officers learn on an indoor range, with targets initially set at 10 yards, then increasing to 15 then 25 yards as they become more proficient with their weapons. It's only after they're proficient with their weapons that they move outdoors, to add environmental effects (wind, sun glare, etc) for the officers to compensate for.