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.
Continuity mistake: At the airport, the aircraft parked at the terminal that they are going to get on is a cargo jet. This is a 727. When they take off the scene shows a A320.
Continuity mistake: When June spills her drink of tequila when sitting in the airplane, there's a big wet spot on her shirt. After that, she goes to the toilet and stays there for maybe ten minutes. When she returns, the shirt is totally dry.
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.
Continuity mistake: In the motorcycle chase, when Roy is right behind Fitz, there is a close-up shot of Roy and June in which, behind them, two beige Smarts turn up. But in the shot afterwards, the Smart has turned black all of a sudden. It can't have overtaken the first car, because the street is way too narrow.
Continuity mistake: When June lies about having the Zephyr and is kidnapped to Spain, they show Fitzgerald driving to Antonio's home (establishing shot). This is before Antonio and Fitzgerald have met, but behind Fitzgerald's car, Antonio is following. Clearly a shot meant for later when Antonio starts to follow Fitzgerald to pick up the package. (01:24:00)
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. (00:06:25 - 00:12:15)
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.