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.
Factual error: The Roswell, New Mexico sheriff forces Bones to examine the body because it was found in his jurisdiction. But later in the episode, we learn that the body was found 2 kilometers from the border of Mexico. Roswell is not even in a county on the border of New Mexico much less one that borders Mexico. In fact the closest border to Roswell between the US and Mexico would be in Texas - hours drive away. The Roswell sheriff would have no jurisdiction.
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.
Factual error: When Bones and Booth go to visit Levi's parents and Sarah's brother yells at her that she is needed at home, when he gets into the buggy you see him wearing a wedding ring. Amish wear a beard to indicate marital status, not jewelry it is against the religion to wear any decoration including wedding rings. (00:08:50)
Factual error: Hodgins makes a remark about the mummy wrappings being for an important person because it is a diamond weave pattern. However, the diamond weave pattern didn't come into effect until the Greco-Roman period that began at 332 B.C. It certainly wouldn't be found in an 18th dynasty mummy, no matter how important he was.
Factual error: Hodgins says that natron was a naturally drying agent, which was used in the second century B.C. This is both wrong and right. While it is true that natron was used for mummification, it was used for thousands of years in Egyptian culture, not just the second century B.C.