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.
Several times the series uses Booth's not having married his son's mother as a plot device, with his access and visitation threatened. However, as the child's biological parent Booth has parental rights regardless of his legal relationship with the mother.
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.
Throughout the series, various characters repeatedly refer to the Jeffersonian Institute as "The Jeffersonian Institution." Although it is technically an institution in the same sense that a college is an institution, "institute" is more correct.
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.
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).