Continuity mistake: When Henry goes to see Clare at the meadow and Clare is about 18 (after he gets the vasectomy) he kisses Clare, and each time they switch between Henry and Clare, the hair clips on Clare are a different color. The first are aqua blue and then they are yellow and back and forth for the duration of the scene.
Other mistake: Shortly after the start of the movie, when Eric Bana's character reappears in the library and starts to put his clothes back on, his pants are already undone. If he had suddenly vanished from the library, then his pants should not be undone (unless, of course, he was up to no good just as he vanished).
Factual error: When Henry travels back to when his mother is still alive and is riding the el train with her, when he gets off the train downtown there are color coded signs on the platform. Specifically, a brown and purple sign indicating that those color trains stop on that side of the platform. This scene took place sometime in the 1970s since his mother was still alive, but el trains were not color coded until 1993.
Continuity mistake: When Henry and eight-year-old Claire are in the meadow talking about the possibility of Claire's parents getting a divorce, watch Claire's left shirt sleeve (audience's right). There is a big white thing (possibly a piece of thread) that goes back and forth from on her sleeve to not there at all between shots.