Axel Foley: I ain't doing nothing in front of this dude, 'cause this dude is a cop! I know when I can smell a pig inside a room. I used to be a Muslim, man, and I know there's pork over here!
In the scene where they are chasing the armored car in the cement truck the chutes on the truck keep going from being down to folded up. This happens several times in the scene.
In the scene where Foley first visits Rosewood's apartment, he at some point pauses and looks at a poster of Sylvester Stallone from the movie "Cobra" (1986). Stallone was originally supposed to star in Beverly Hills Cop (the first one) as Axel Foley (or his name was going to be Axel "The Cobra" Cobretti). The script was changed for Eddie Murphy, removing a large amount of the action sequences from the movie. Many of those sequences were later used in "Cobra." The shot of Foley looking at the poster is a reference to this fact.