Continuity mistake: All the inside shots of both cabbies driving show the interior color is tan and brown, but in the scene where Pike is hanging out of the cab as it's driving away one cab's interior is two tone green. When they open the doors at the crash scene with the chief's car at the end you can see the other car has a silver and black interior.
Continuity mistake: During the opening scene, Smiler passes Milton Berle, loses control of his car, crashes through the barrier and up the ramp. However, when Berle et. al. stop at the spot where Smiler supposedly left the road, the two spots don't match. The broken guardrail where Berle is standing is not the same spot where Smiler broke through. The second spot is roughly 100 ft. up the road from where the car went "sailing right out there".
Continuity mistake: When the case is found and opened for the first time, the bills are in bands. However, when the case opens on the fire escape, the bills flyout individually.
Continuity mistake: The two 1959 Plymouth taxis keep changing from scene to scene; in some you can see cab numbers painted on the hood and trunk, and in other scenes they aren't there, also dents on the cars show up and later they are gone.
Continuity mistake: In the opening scene, Smiler passes first the truck and then the Volkswagen but then passes 3 other vehicles before he passes the Imperial. Two of the 3 cars are never seen again. The 3rd is a light cream Chrysler station which is supposed to be the '62 blue Plymouth wagon of Sid Caesar.
Continuity mistake: Spencer Tracy says they will go to the crossroads and turn south (a right-handed turn according to the wall map he's looking at). When they get to the crossroads, they all turn left which would be north.