Continuity mistake: The person responsible for background shots while anyone is in a car driving, is grossly negligent in their continuity. Very rarely do Bones & Booth drive down a street without the background changing rapidly from urban to rural streets, and back. In a Season 1 episode, they're driving through a flat desert, with nothing in the background except scrub - and then suddenly, a mountain appears in the middle of the shot.
Revealing mistake: The producers have not taken enough generic shots of the places the gang hangs out at; the Royal Diner, & the Founding Fathers. If paying attention (or, watching multiple episodes in a row), one will notice the same people wandering down the street an awful lot! As well, outside the Royal Diner, there's a weird-shaped street corner, that appears to force all traffic in front of the Diner. This would be due to the size of backlot being limited, and certainly doesn't look right.
Character mistake: Sweets is a psychologist who deals with the team's problems. However he is constantly shown breaking patient confidentiality by mentioning what has been said in sessions.