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.
While in the diner, Angela refers to a python as being an "Articulated Python" instead of a "Reticulated Python".
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.
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).
Several times, Brennan is seen riding in Booth's car with her window rolled down. Her hair should be blowing in the wind generated by the speed of the car, but it never moves.
Throughout the series, x-rays show the shadow of flesh around the bones, even when the remains were only the skeleton when found.
In several episodes, there are scenes that take place from inside a moving vehicle, where the outside is seen from either the side windows or rear window, are clearly rear projection.
When they lay out the bones of the murder victims on the table, they do it in such a way that has them in the correct positions relative to how they are when alive. However they have the bones in the hands and forearms placed inaccurately. They set them out palm side facing down flat on the table, with the thumbs pointing toward the body. This position makes the two bones in the forearm (Radius & Ulna) crossover each other. But seeing as those bones are laid out in a straight position, the bones of the hand should be palms facing up with the thumbs pointing away from the body. The radius and Ulna are correctly positioned in relation to the hand, but not relative to the body itself, therefore should be swapped around too, with the Ulna closest to the body and the Radius on the outside.
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.
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.
Several times Booth is shown at the firing range without hearing protection, eye protection, or both.
Throughout the series, while the characters are in the J Edgar Hoover building, it is very inconsistent of when they wear badges. Booth almost never wears an ID badge, Sweets almost always wears one, Bones wears a visitor badge most of the time, people brought in for questioning are about 50/50 on wearing a visitor badge or not. As it is a federal building after 9/11 wearing a ID badge is required.