At the funeral, the commander of the Honor Guard gives the command "port, arms." The honor guard goes to port arms, i.e. lifting the rifle from the ground and holding it diagonally in front of the body. He then gives the command, "Ready, Arms." The honor guard is shown lifting their rifles again, when they would have already been holding them.
When Dr. Saroyan brings up the computer monitor showing security footage, the skeleton is visible on the vault door in the lower left portion of the screen. However, in moment before and during the explosion, a moment before the security cameras go blank, the skeleton is already missing from the screen with the vault door.
While in the lab and wearing his dress blues, Booth's ribbons change order. In one shot his lowest medal (bottom row closest to the actor's left arm) is the Kuwait medal issued for Desert Storm. In the next shot his lowest medal is the Bronze Star (it appears his "fruit cocktail" of ribbons was put on upside down for this shot).
When Zack is in the hospital, Cam tells him one of them will be with him at all times and Angela says its because they love him, the close up on Zack shows Hodgins's hand rubbing Zack's shoulder and then head, when the camera pans out we see Hodgins rubbing his shoulder and then head again.
When Bones leaves Booth's bathroom he has his cigar in his hand but in the next scene it is in his mouth.
When Bones confronts Booth in his bathroom he stands naked in front of her without covering himself. Bones says it's refreshing his Puritan values didn't cause him embarrassment. Sexual modesty was a particular attribute of the Victorians, not the Puritans, and a learned anthropologist like Brennan would know this.
At the hospital Zach refuses to use the morphine pump to ease his pain. Hodgins ignores his request and repeatedly presses the button on the pump until Zach passes out from the pain killer. However, such pumps are programmed not to over medicate, in order to prevent patients from accidentally overdosing.
In the beginning of the last scene in the hospital Cam describes the shapes of the Greek letters pi (lower case), beta (upper case) and alpha (lower case) and remarks that she does not understand what they are. Any medical doctor would know those letters as they are used in physics, statistics and calculus, courses any medical student would have to take prior to getting into medical school.
The missing bones in limbo are from a man who was "180 centimeters" according to Dr. Brennan. She says this is the equivalent of a person being five feet, eight inches. Actually, a person would be around five feet, 11 inches (5'10.866'')- a mistake Brennan wouldn't make.