Other mistake: In Havana, there is a secret car in an underground bunker, a mini. When you find and drive the car you can do a burnout, but the smoke comes from the rear wheels - no minis ever had rear wheel drive.
Continuity mistake: Some of the missions - unintentionally - let Tanner switch cars if the player is quick enough (by stopping at red lights and swiftly jumping into another stationary vehicle, for example) and leave the default vehicle behind. Still, in the following CG cutscene, it's always the default/generic car that can be seen.