At the party, as Cole is about to drink his "frabble," his cup disappears when the shot cuts.
During the scene when the suspect is about to jump onto the freeway, there's a sign on the bridge which says Ocean Blvd and in the background in some of the shots there are green street signs. Los Angeles doesn't have an Ocean Blvd nor green street signs.
Murtaugh's father-in-law claims to have originated the phrase "follow the money", although it was used in 1976 in All the President's Men (1976).