Continuity mistake: In the scene explaining the history of the missing jade elephants, they are described as being given to ambassadors by the emperor Zhu Di of China when the Forbidden City (in China) was first opened to foreigners in 1421. When the elephants are all brought together, the representative Daichi Yoshida from the Japanese embassy comes to pick them up, describing them as "a priceless piece of our history."
Continuity mistake: At the end of the episode, the Mercedes S class that is burning is not the same car that Castle drove previously in the episode, it's an older model one. Either it's a mistake or has to do something with the plot resolution, decide yourselves...
Continuity mistake: 1.08 (Depraved Heart) Lightman is working late and his daughter drops by to bring him Thai food. As she's walking towards her father, her arms are crossed. Cut to the immediate shot from behind, and her arms are down at her sides.
Continuity mistake: When Pete and Myka first get to Warehouse 13 and walk up, the football that flew at Pete is lying on the ground close to the open door. In the overhead shot, the ball is gone, but is there again in the next closeup.
Continuity mistake: When Deeks is shot in 2-17 "Personal", his records show no next of kin. However in later episodes he has a mother.
Episode #3.1 - S3-E1
Continuity mistake: DI Chandler calls a suspect "Daniel Wilkie." However when the interview is done he goes and talks to Ed, saying "you've just arrested Ben Wilkie."
Continuity mistake: In the scene in the courtroom towards the end where Alicia is talking to the security guard who is in the witness stand, he glances over at the jurors. When they cut back to the jurors a few seconds later, they are wearing different coloured shirts. (00:33:30)