When Brennan and Booth first meet Harold ("mayor of mole town") he has the brown bag of food in his arms, then they switch to a shot showing his back and he is swinging his arms which indicates that he doesn't have the bag in his arms, and then when they return to the front side of Harold he is holding the brown bag.
When Angela is talking to bones about not feeling comfortable talking to the mole person her arms are at her sides but in the next scene they are now crossed in front of her.
Hodgins, in describing the head wound of the Civil War era tunnel skeleton, mentions bird shot "pellet size 12, 0.73 inches in diameter, made of lead". First, size 12 shot is .05 inches in diameter. Second, think of a 45 caliber bullet, a big honking bullet. It is 0.45 inches in diameter; that is what caliber means. A single piece of lead .73 inches in diameter (75 caliber) would completely fill the barrel of a large shotgun.
Dr. Goodman exclaims that the seal was placed in a vault in or soon after 1779 in Washington DC during the American Revolution. Washington DC wasn't established until 1790.
When Dr. Goodman examines the roman artifact, he looks at it under a lit magnifying glass. However, the light is facing his face. The light on this type of instrument is supposed to be facing the object you're examining, to make details easier to see. If the light is facing the observer, all it does is light up the observer's field of view, preventing him from actually seeing the object.
When Dr. Goodman explains that Harold has given Angela a description of a Raeburn portrait, she doesn't understand the reference. Throughout the series, it is established that Angela is not only a good artist, but has extensive art history / technique knowledge. While she may not have instantly recognized that the sketch resembled a work by Sir Henry Raeburn, she should have understood the reference once Dr. Goodman points it out.
When Dr. Goodman explains the vault seal is a sigil he mispronounces the word with a hard g rather than a 'dg' sound like in 'edge', this is not a mistake a archaeologist would ever make as the word has only one accepted pronunciation.
In the discussion of the fatal attack as it's animated in the holographic display, Angela and Zack agree that the injury is on the victim's right, indicating a left-handed killer (which is later shown to be true). However, the injury is shown throughout as on the left rear of the victim's skull, and the animation is clearly that of a right-handed attack.