Plot hole: Most of the story depends on Costa coming forward as a witness; however, he would have had no reason to do this. It would only make his goal of assuming others' identities more difficult.
Suggested correction: Some serial killers try to involve themselves with the investigation, for instance famous serial killer Ed Kemper.
Continuity mistake: During the love scene Ethan has his left hand on Angelina's throat, but then it changes and it is his right hand.
Factual error: During Angelina and Ethan's "love" scene, they climb onto the table and smash what is quite obviously break away glass. No glass smashes that easily when merely touched.