The seal on a police car implies that the LAPD was founded in 1781, the better part of 100 years before the Union took possession of California.
27 minutes and 14 seconds into it, the cop tells Michael, who is riding in the back of the cop car as a ride-along, to come on up to the front seat Michael proceeds to open the back door from the inside. You can't open the back door of cop cars from the inside, that way the prisoners can't escape.
Pete and several cops in the film are wearing pistol skill medals on the wrong pocket flaps of their uniforms. Actual LAPD officers wear the medals on the left pocket flap below their badges. Pete's is on the right pocket, next to his nameplate.
The alarm password to Micheal and Karen's home should have been changed immediately after it's discovered that Pete is psychologically impaired it should not have been left the same allowing Pete to stalk enter plant drugs in the home and frame Micheal..
Given all the noise, screams, alarms and gunshots, you'd think the street would be full of neighbors wondering what was going on, but it's deserted when Karen opens the door and sinks down on the porch, and remains so until the cops get there.
When Michael is speeding home in his lawyer's car, a motorcycle cop starts chasing him, and follows him all the way home. So why didn't he pursue him straight into the house? Presumably, the lawyer must have explained what was going on, but it took an unrealistically long time for the cops to show up.