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)
The Thing You Love Most - S1-E2
Character mistake: Regina says to Emma that her apples are from the Honeycrisp tree, but Regina's apples are not Honeycrisp apples, which have a different color and shape. (00:03:10)
Character mistake: In the newspaper article that Emma reads, Kathryn Nolan's first name is misspelled "Katherine." (00:19:45)
Answer: He knows who she is because he knows that the fairy tales are true. He was also shown to sneak out to go see Emma or someone else. Sometimes he succeeded, sometimes he didn't. This is how he knew to look for her despite his strict mother.