In the karaoke scene PJ takes off her hairpin with her right hand while holding the microphone in her left. In the next shot the microphone is in her right hand and the hairpin is in her left.
Just over 53 minutes in, Harry Deane is shuffling along an outside ledge of The Savoy, facing the wall, with the stolen, large Ming vase. To continue, he must climb over a metal obstruction. He puts the vase down at arm's length on the right hand side of it, over a stone block away, climbs over it but gets his trouser leg caught on it. The film cuts to a car scene and when it returns to Harry his trousers are still entangled and he is taking them off but the vase is now placed right against the obstruction.
The stunt double used for PJ in the calf roping scene is heavier than Cameron Diaz.
About 59 minutes in, Harry and PJ Puznowski are arguing quite loudly in the bedroom, whilst PJ Pusnowski is also engaged in a conversation with Lionel Shabandar who is in the main room/lounge and whose voice can also be clearly heard. If she can hear Shabandar speaking and he can hear her, then he would obviously be able to hear them arguing too but clearly does not.