Continuity mistake: After June follows Roy in the middle of the night, she gets taken into the secret service. Out the back windows, it is pitch dark. Out every other window, striking daylight shines through.
Audio problem: During their conversation on the plane, when Cameron Diaz tells Tom Cruise about the wedding gift for her sister being a car, during shot when she says "kinda like a present from my dad too you know" you can see her mouth doesn't move. It's not because of the angle of the shot either; you can see her mouthing moving from the same angle during other parts of the conversation.
Other mistake: When June is standing on the escalator in the airport the people on the escalator with her swap from shot to shot as they change camera angles from a view looking down at her to one taken from the side. In one scene the escalator is nearly full with people, but in the next there are only two men standing behind her.
Continuity mistake: The plane that took off when Cameron boarded has its engine on the wings. In the external view of the same plane when Tom was fighting the bad guy, the engine is on the fuselage.
Continuity mistake: During the freeway car chase, Roy lands in a convertible with a Great Dane in thee front passenger seat. In the next shot, the dog is transformed to a shaggy dog.
Continuity mistake: In the scene after June and Roy are riding on top of the car carrier truck, the CIA Director is reviewing a security tape of the diner abduction. You can hear Roy say "Pies for everybody, everybody gets pies", however, the video on the playback monitor at that exact moment shows him shooting the booth above Rodney's head. Roy didn't mention the pies until several seconds later after he kicked the server who made a noise. You can even hear the gunshot after he says "pies for everybody", then the CIA Director pauses the tape.