Continuity mistake: In the scene when Richard Gere is trying out the video camera before he and Diane Lane begin to fool around, the camera box disappears and reappears on the bed.
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.
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.