Deliberate mistake: This has the old T.V. show style "it was 6 a.m. on January 7th we ... " beginnings to the scenes. Pay attention to those times and dates. They're not even close to being in sequence. I mean days, not just times.
Deliberate mistake: When the board member is shot up in the beginning by ED-209, in one or two shots you can see the bullet impacts happen about 1/2 a second after the shot starts (Criterion DVD version). (00:11:55)
Deliberate mistake: At the end of the film, two officers attempt to surround and handcuff Joshua. Using two officers to cuff someone is NEVER done for the exact reason of what ends up happening, as Joshua manages to grab a gun from one of the officers. Only one officer would have been doing the deed in the real world, but it's clear this error in being completely against police protocol had to happen so the good guys could prevail over the villain.
Deliberate mistake: Proctor and Harris were surprised when they walked into the Blue Oyster and found out it wasn't a restaurant, but in Police Academy 2, Proctor apparently knew not only the bar, but the address as well.