When Booth breaks into the Jeffersonian and is tackled by the GSA men, it clearly shows his weapon flying across the floor toward the door (16:47). However, it the close-up scene (16:51) the gun is clearly visible being held by the barrel by one of the GSA men. (The hammer still cocked).
Bones mentions that JFK was never known to have osteomyelitis. In reality, he was diagnosed with it by his personal physician. The location of the osteomyelitis is inconsistent with this diagnosis, though, as JFKS's diagnosis was in the lumbosacral spine and pelvis whereas the skeleton's was in the arm.
When viewing the playback of Booth's shots at the cantaloupes Hodgins says "1.6 seconds exactly" but the time displayed on the monitor is 1.15.