Revealing mistake: During the windy scene in new york, just after she falls for the first time and after she hits the taxi trying to stop it. If you look in the background there is a guy with a bike. Long black hair, barely affected by the winds that are throwing her and other people about. (00:06:00)
Continuity mistake: Edward completely wrapped Paul's body up in a rug and wrapped the rug with tape. When the body is shown in the dump, Paul's right arm is exposed from it, although, the tape is still wrapped around the rug. (01:39:00)
Other mistake: When the son is going to the potty, you hear him peeing but there is no stream of urine.
Continuity mistake: At the start Ed has a blue shirt on. He leaves the house with his son - when he turns to wave goodbye the shirt has turned grey.
Other mistake: When the police arrive at the house the marked police car had Ardsley Police on the side. The other vehicle was unmarked. Charlie tells his mom it's NYPD before the detectives come into the house and introduce themselves. (01:34:00 - 01:35:00)
Answer: Although Connie wanted them to go to Mexico and assume new identities, it is implied that Edward, who initially goes along with that idea, will likely turn himself into the police. However, there's no definitive ending given, so the audience is left to interpret the outcome.
raywest ★
An alternative ending was shot in which Edward says goodbye to Connie in the car and walks into the police station. The director discusses this on the commentary track. The alternate ending is on the DVD.