While Pam is waiting for Booth in the interrogation room, she is sorting her trail mix. In one shot it is completely sorted, but in the next, it's half sorted.
Temperance says her mother told her she sings better than Cyndi Lauper, who plays the character Avalon in later episodes.
EDIT: This is not an error in continuity because Bones' mother didn't say she sang better than Avalon. In the Bones Universe, Avalon and Cyndi Lauper are two separate individuals.
(at around 48 mins.) Doctors Brennan and Hodgins are walking and talking together and as they approach the secured, elevated, work area Dr. Hodgins reaches for his I.D. and successfully scans it so they might enter without setting off any alarms. However, the magnetic strip on the card is on the edge of the card that is in his hand, not on the edge he swiped.
When Booth is shot, Bones puts pressure on Booth's wound while Hodgins tells Zack to call 911. Cam is an MD and yet she stands in shock several feet away rather than rendering medical care.