When Copeland and his partner have Arnie and Kyle blocked off in the alley, Copeland's partner's voice is heard radioing Captain Harris, although his lips are not moving, nor does he even pick up the radio.
In the television version of the movie, an escaped criminal is thrown from the hood of a police car, and is apprehended by Callahan. Although she applies handcuffs to the criminal in close-up, a wide shot reveals the handcuffs are secured around only one of his wrists, as he is holding the unsecured cuff in his free hand behind his back.
When House sits on the bench, catapulting Sweetchuck into the basketball hoop, a wide shot shows that the bench is several feet away from the wall where the basketball hoop is, making it impossible to enter the hoop from underneath at that position.
At the beginning of the movie, we see Harris inadvertently walk into the shower room after speaking with Mahoney. There is an immediate scream of surprise and Harris exits the room drenched. Later on in another scene with Harris, we see that the showers are in individual, unmistakable shower stalls and are a distance from the shower room door. Harris would have (1) recognized this as a shower room and (2) even if he hadn't, there's no shower head directly inside the shower room door to walk under right after entering the room as Harris evidently did.
Proctor's Port-o-Potty is lowered into the stadium full of people, and the housing of the unit is lifted, leaving the base and Proctor. When the music plays, Proctor stands up and you can briefly see his underwear (which he wouldn't be wearing because he was using the toilet).
Proctor bites into a hamburger and squirts ketchup onto the pants of a fellow officer a few feet away. One, the container it squirts out of can clearly be seen between the hamburger buns, and two, ketchup otherwise is not a projectile condiment.