Revealing mistake: During the car chase scene, if you watch the speedometer on the car, it never rises above zero. That, and the obviously poor image quality of the "road" in front of them, shows that they were using projected film in front of the car.
Revealing mistake: The Union Flag pinned to the back of the taxi driver's jacket is upside down. Since he is part of the government (he's undercover for the Foreign Office) he shouldn't make such an terrible mistake. (01:20:40)
Revealing mistake: In the bull ring scene, in the close up shots it's Raquel Welch, in the pulled back shots it's obviously a stuntman in drag with her voice dubbed in.
Revealing mistake: When the sky bike is flying during the competition it is obviously suspended from a crane as you can see the wires.
Revealing mistake: When Dr Dolittle is talking to the parrot and it raises its left leg, you can see a piece of string running past Dolittle's head used to raise its leg.
Revealing mistake: Despite the best efforts, you can tell the fabled white rhino is just a prop on wheels.