The Jeffersonian Institute is located in Washington DC. The establishing shots of the building show palm trees. There are no palm trees in the District of Columbia.
When confirming heights of patients from SI units to Imperial units, one victim is said to be 180cm, but Dr. Brennan said it was 5' 8". 180cm is actually 5' 11".
Several times Booth is shown at the firing range without hearing protection, eye protection, or both.
In season one Brennan says that she was in the foster care system till her grandfather got her out; in later seasons she claims not to have met her grandparents.
When Bones and Booth are driving together in the dark SUV and they get a phone call that requires them to change course, footage of their truck is shown making a U-Turn. This is the same footage used over and over in at least 2 seasons, in almost every episode.
Characters routinely refer to interstates in the D.C. area as "the 64" or "the 81". People who actually live there omit the article. They say "64" (most common) or "I 64" (less common). The use of "the" is a West Coast thing.
In one episode, the lab techs use stereo-lithography (3D Printing) to replicate a set of bones in seconds. To do such a task in real life would take hours to an entire day.
Several times throughout the series, Brennan mentions Booth's claim that he is a direct descendant of John Wilkes Booth. That would be impossible, according to ancestry sites John Wilkes Booth had no children of record, and only one of his brothers had a son who survived to adulthood, and the direct male Booth line died off after that generation. Only a few Booth sisters had sons with other surnames.
While in the diner, Angela refers to a python as being an "Articulated Python" instead of a "Reticulated Python".
Max Keenan/Matthew Brennan's Inmate Number is 90-A-0133. This is a New York Dept. of Corrections number. Keenan was in Federal custody, which would have given him an 8-digit numeric inmate number. Keenan was portrayed as a state inmate, but was in fact federal. Also, the 90 in his NY state number indicates Keenan had been arrested in New York in 1990, one year before abandoning his children, which was never alluded to in the series.
During the title sequence, when David Boreanaz is presented, the "FBI" label on his jacket is mirrored. The entire shot is mirrored from the one actually shown in an episode, though, for artistic purposes.
In several episodes in Season 1, the red and blue police lights in the rear of Booth's FBI Tahoe are installed incorrectly so that the lights face the interior of the vehicle. Its best seen in 1.20, when they're driving to the small town. If the lights face the interior of the vehicle, they obviously cannot be seen outside of the vehicle (plus they probably blind the occupants of the vehicle).