When Esposito brings up the picture on the computer of Evan Mitchell from the police database, his stats say he is 5' 9", yet we can clearly see from the mugshot that his head goes over the 6' mark.
Castle and Powell illegally break into the apartment, Castle shuts the door, and the two walk into the room. However, when Beckett arrives at the crime scene, she unlocks the door....something the men obviously have already done.
The thief is running away on the ground floor of the building, then in the next scene he falls from a height on to the hood of the police car where Castle is sitting.
When Beckett is questioning Evan Mitchell, the first thing he says is that he won't talk without his lawyer. She continues questioning him, which means even if he had admitted to anything, it wouldn't be admissible in court.
When Castle and Beckett get into the elevator while talking about the "Beckett Onion," a crew member can be seen in the reflection on the elevator doors.