Lancaster disarms two agents by putting his car into reverse and slamming into their car in a narrow alley. Then he pulls forward and does it again. But on his second pass, there's a shot of the back of his car completely undamaged before it makes the second hit. (In that final shot, the car is damaged as it should be.)
Burt Lancaster holds out a folded 100 dollar bill to give to the ticket window employee but somehow in the very next shot it gets straightened without him moving his hand.
All of the dialog was dubbed in post - in fact it seems all of the sound was done in post-production. This leads the sound in the whole film to seem a bit "off" and thin.
In the alley just prior to the rear-ending of the tail car the tail says "I can't see him, he must have got out and run" yet Cross' car's brake lights are clearly on, meaning somebody is in the car with their foot on the brake pedal.
Early in the movie, the two CIA covert operatives are openly discussing a high profile political assassination on-board the airplane in close proximity of civilians' ears, including names and motives of involved parties. Though it helps the audience understand the story, that kind of conduct is virtually impossible in real life behavior.