Plot hole: How did Catherine manage to show up at the original crime scene at the same time that the detective arrived? He came from across town; she came from Europe, as proved by her "jet-lagged" comment the next morning.
Plot hole: The beach could be reached only by vehicle, but they only had one car and they arrived separately.
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.