Joe's weight changes throughout the movie, as can be seen by the size of his neck. Matthew Perry's weight was changing because of his drug addiction while he was filming (see Trivia).
After Tony and Kate serve Sara, the Polaroid picture is visible in Kate's hand. It features a large Texas flag that was not in the room.
When Sara originally makes up the "contract" between herself and Joe, she does not sign her name on the bottom, writing only "One Million Dollars". Later on, when Joe shows her the contract, her name is signed on the bottom.
There are many indications that the movie takes place around Christmas time, but near the end of the movie, as it is approaching 7pm Texas time, it is still daylight outside when it should be dark.
When Matthew Perry jumps down from the top of the elevator, his stunt double is wearing a red cummerbund. When Perry pops up acting as if he was the one who had just jumped, his cummerbund is black.
The legal goofs in this movie are hard to count, but to start with, in New York, the rule is that when serving process on someone, all you have to do is mail it to them and tack it on their door. Sara's running would have no legal effect.
When Kate allows Joe into the house to use the bathroom, her lips aren't moving, she's just smiling as she closes the door. But her voice is heard saying, "I'll show you where it is."
Bangor, Maine is mispronounced by Matthew Perry.
When Joe and Sara are up in the booth at the Union Arena, he calls her "Cheryl".