Continuity mistake: When Beckett, Esposito and Ryan interview the fruit stand vendor, he states that he saw a bronze Mercedes drive by, to which Esposito replies, "That's Castle's car." In the previous scene at the car crash site, Ryan asks Esposito to check the back corner of the car for damage, which is silver or gray, not bronze, in color.
Continuity mistake: When Castle is allowed to talk to Mrs. Ruiz's second graders, as he enters the classroom, he is hit in the temple with an object thrown at him and holds his hand to his head in pain. After he turns to say something to Beckett, as he turns back, not only has the hand on his head switched, it's also much lower, down on his chin.
Continuity mistake: When Beckett brings Castle to the campsite, he tells her he never would have set up camp near the ocean because of his research for Tropical Storm, and his irrational fear of tsunamis. Beckett then says to Castle, "You bought a beach house in the Hamptons." To which Castle replies, "Yeah, on the inland side, not the ocean side." But in 5x04 [Murder, He Wrote], Castle gives Beckett a tour of the Hamptons house, finishing out to the backyard with the sounds of waves crashing, and Castle saying, "This is actually my favorite part. The sound of the ocean, complete privacy..."