Continuity mistake: During one of the scenes when Brad Pitt arrives home, he is driving a Lincoln Town Car, not his Cadillac. This is the car that he doesn't get until later, when he steals it and drives home during the scene when they crash the cars into each other at the end of the driveway.
Deliberate mistake: When Brad Pitt is in his garage and cleans the spot on this collar, he should have turned the car's mirror to the left to see himself. Instead, he turns the mirror to the right so the camera can get a view of his collar. (Yes, it's a common filmmaking technique, to show viewers what he's looking at, but it IS still a mistake.)
Factual error: While John is crawling through the sewer pipes, Jane's monitor shows his GPS location as 47.28 N 12.46 W, 35 feet below sea level. This places him under the Atlantic Ocean, somewhat north of the tip of Spain - nowhere close to New York, or any other streets for that matter.
Continuity mistake: After the botched hit in Mexico, Jane returns to her office, a little beaten up, and her associates tend to her wounds. Particularly clear is an injury to her right shoulder - it has bled enough to mark her singlet top, and is covered by a large piece of plaster. Yet when she dances with John in the restaurant, only a few hours later, there is no sign of plaster or wound.
Revealing mistake: In the scene where Jane is trying to run over John with her car, she jumps from the driver's seat while John is in the back of the car. Right before the car crashes through the fence, you see John through the back window. You also see a head in the driver's seat, even though no one is supposed to be driving the car.
Continuity mistake: When John and Jane steal their neighbor's minivan (after their house explodes) and back out the driveway, an assassin jumps onto the back. John hits the brakes and the assassin falls off onto the ground beside the van. In the next shot it is implied that the van runs over the assassin (two bumps), but John has not turned the steering wheel.