Other mistake: After Edward kills the boyfriend, there is a scene where the family is having what appears to be Thanksgiving dinner. If it really is Thanksgiving, the timeline doesn't make any sense, since the rest of the movie appears to be in the spring time. For example: When the cops come to Diane Lane's house for the second time, she and Edward are working in the garden, and they remind her that she was in SoHo four weeks prior. Certainly someone wouldn't be working in the garden a couple weeks after Thanksgiving in New York, unless the line about "four weeks ago" is an error.
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.
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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.