Plot hole: Series 9 episode 12: "Agent Hartford" had no fingerprints: the FBI "removed" them. But when they find the street piece that Vinny had, they dust it and say that Hartford's prints were all over it. This might be OK, if he were a real agent on the books (but they never heard of him at Quantico), or if he were a real criminal - but in that case, they would have sussed it all out earlier.
Factual error: When Nick picks up the contact lens from the PI's body, you can tell from the way it bends while he is holding it with the forceps that it is soft and pliable, as if it had just come out of the eye. However, after 6-12 hours outside of an eye or a contact case (the amount of time David says the PI has been dead), a soft contact will dry out and become wrinkled and hard.
Plot hole: Episode 9-18, "Turn, Turn Turn": Greg states that the dead motel manager crawled up into the ceiling the same way that he did, and you see Nick open the access panel in the ceiling. The manager couldn't have closed the ceiling panel after him and no one was managing the hotel in the week he was missing. The panel should have been open when Nick came into the room. The new manager stated he didn't know if there was a panel in that room, since he just got there.