Continuity mistake: The number of plastic self-adhesive stickers attached to the left side of the contract change. After the contract is flopped onto the table and just before Crown signs it, the first side view (very quickly) shows 3 stickers attached to the left side of the paper with red on the bottom. Crown pulls the pen from his jacket. No one touches the contract. The second view shows 2 tabs attached at the same place with red on the top. (00:00:08 - 00:07:58)
Continuity mistake: In the glider scene, Thomas Crown's watch switches back and forth between his right and left wrists.
Continuity mistake: When Renee is sipping coffee and watching Thomas Crown far below on the street running to his car, in her first look, the car is parked at a 45° angle headfirst against a rounded curb with two police cars to its left, but in the second snippet, when she looks, his car is parked across a street, as any car would be parked and with a sidewalk to its right. The rounded curb scene and the two cop cars are gone.
Continuity mistake: In the restaurant having dinner Rene's pearl necklace starts untwisted then twists and later untwists. To do this that necklace would have to be unclasped and manually twisted.
Character mistake: Thomas rips off his one glove as he makes his escape but then grips the bottom edge of the security door to slide under it. Smooth metal door would leave perfect finger and palm prints. I doubt detectives would miss prints on a door that was normally recessed away from the public. His prints may not be on file but would be easy to obtain once he was under suspicion. (00:19:20)
Answer: On the commentary track for the DVD the director states that he has no idea how Thomas Crown stole the final painting.