Continuity mistake: Neal chats with the publicist while Burke goes to meet the journalist. Her hair is either tucked behind her right ear in shots from the left, or not in shots from the right.
Other mistake: When Neil is in prison and has time on his hands, he puts pieces together that were shredded. Neil's name in the file is CAFFERTY, not CAFFERY. Also, in the same scene, the words "e've" can be seen with the W missing. Yet, later on, when Neil shows Burke the final photocopied piece, the W that wasn't there is now visible.
Character mistake: If you look at the piece of paper Neil takes from Agent Matthews the word "warrant" is misspelled as "warreant". (00:21:20)