Character mistake: Gendry gets declared as Lord Gendry Baratheon of Storm's End by Daenerys. But he refers to himself as Gendry Rivers - the surname given to bastards from the Riverlands. Gendry comes from King's Landing, and bastards from there are called Waters, not Rivers. Given that Gendry is not an acknowledged highborn bastard, he should never have had a surname in the first place.
Character mistake: In the evening, Emma states that Kathryn Nolan has been missing for 24 hours, meaning that this episode takes place the day after Kathryn disappeared. When Emma investigates Kathryn's car, David tells Emma that he last spoke to Kathryn "yesterday afternoon" (and stresses that he is telling the truth), and that he hasn't spoken to her since he ended their relationship. However, "What Happened to Frederick" establishes that David broke up with Kathryn the day before she tried to leave town and disappeared, because when Kathryn apologized to Regina, Regina referred to the events surrounding the break-up as "what happened yesterday." Emma checks Kathryn's phone records and finds out that Kathryn talked to David on the phone the day she disappeared, but David could not have referred to that conversation, since "Red-Handed" and "Heart of Darkness" both establish that he doesn't remember the phone call because of a memory blackout. Making matters even more complicated is that when Sidney shows up with the phone records, Emma specifically says to him that David told her that he DIDN'T speak to Kathryn that day, which, in fact, he said he did. (00:12:45 - 00:26:45)
Character mistake: Iain and Mickey tell paramedics about an old lady needing immediate help in her apartment on the "5th floor" just before stealing their ambulance as the paramedics storm into the building. However, the apartment building has lots of units on every floor and no unit # was given in this fairly large building. Medics would have trouble finding her had this been a real call.