Continuity mistake: In this episode, Booth and Bones are telling Sweets about their "real first case" together - the case where they actually met for the first time. During this episode, Booth, Bones, and Angela take some evidence to Caroline, and Booth introduces them both (most importantly Brennan) to Caroline. However, in season 1, episode 19, "The Man in the Morgue", (which would have taken place after this initial first meeting) when Brennan is accused of murder in New Orleans, Booth has Caroline fly to NOLA to be Brennan's lawyer, and he introduces the two of them. If they had already been introduced during the first case Booth and Brennan worked on together, they would not have needed to be introduced here; they would have already known one another.
Continuity mistake: It is the evidentiary hearing, all characters are put on the witness stand so you get to see what all of them are wearing. The trial starts the next day and lasts at least three days, but when they are in court at the end of the trial for the reading of the verdict for the gravedigger they all have the exact same outfits on as the day of the evidentiary hearing.
Continuity mistake: When Brennan and Hodgins are in the aquarium tank recovering the skull, the hose for Brennan's air starts over her left shoulder. During the first close up where Brennan is actually retrieving the skull, the breathing apparatus has been reversed, so the hose is now over her right shoulder. All other shots the hose is over the left shoulder.
Continuity mistake: Near the end, as Parker drinks his milkshake, its contents rise & fall (not counting his drinking some). Also, he moves the glass about enough to illustrate that it's fake - it would have spilled, the way he handles it.