Capt Holly (Charlton Heston) twice refers to the sniper's weapon as an "automatic rifle" (a rifle that continues to fire as long as the trigger is held back). But the weapon is actually a semi-automatic (in which only one shot is fired per trigger pull). A real policeman would not have made such a mistake in basic firearm nomenclature.
When Pratt, the SWAT team member, is climbing up to the stadium lights platform, he is first shown in a long shot climbing up the fixed rung ladder attached to the platform's support pole. A close-up then shows Pratt climbing up the steel extension ladder that he used a moment before to ascend to the support pole. A wide shot then shows him ascending the fixed rung ladder on the support pole again.
When Sgt. Button and Lieber pull down and arrest the spectator who is sitting on the platform underneath the lights, the spectator's hands are free when they pull him down into the seats. In the next shot, as the spectator lies on his stomach in between the seats, his arms are bound behind him by twist-tie handcuffs. In the next shot, his hands are free, and Lieber is putting the twist-tie handcuffs around the spectator's wrists.
While moving into their firing positions at the stadium, several SWAT members have their fingers on the triggers of their M16 rifles. This violates a basic rule of gun safety, which says that the finger must stay off the trigger until the sights are on the target. Until that time, the finger should be placed alongside the trigger guard.
Near the end of the movie, Sgt Button and Capt Holly are stalking the sniper in the tower where he is hiding. Visibility is almost nil because of darkness and the smoke from a smoke grenade, yet the two officers are wearing sunglasses. All this would have made it near impossible for them to see the sniper, yet Holly spots him immediately and shoots him.