When Murtagh is doing his Godfather impression to Trish, her glasses are in her hand in one shot, and on the table in the next.
When Cole picks the lock to the door of the vet clinic, he only uses one pick rake when two are needed.
Just before the scene with Cole, Murtaugh, and Barnes in the diner, the exterior shot shows the Denver Diner, located in Denver, Colorado. The shot even shows the signpost with the correct cross streets of West Colfax Avenue and Inca Street. This diner is most definitely not located in Los Angeles.