In several scenes, Temperance has shorter straight hair. In others, her hair is longer and wavy/curly. The scenes take place over a few days and her hair could not have grown that much.
When Brennan calls Zack over to examine the anomalous piece of bone, she is holding the fragment. The camera pans out and her arm is extended, possibly pointing at the ground. When it zooms back in, she is again holding the bone close to her face.
The names on Bones' parents file says Matt(not Max) and Christine Brennan.
When starting the wood chipper to feed the frozen pig through, the start button is pressed with an open palm. The start and stop buttons are together in a recess to avoid accidental hitting and would not be activated by an open palm.
Dyson of the NTSB is describing the jet crash, saying the jet reported problems while "200 miles southeast of Norfolk. Yeager Airport of Charleston tracked them for 30 minutes". Norfolk is in Virginia; Charleston is in WEST Virginia, a different state. Yeager Airport would not be tracking a plane 500 miles away.
As Bones arrives on the crash site the agent in charge tells her that "at zero four hundred last night....". 04:00 is 4 AM and he should have referred to the time as "at zero four hundred today (or yesterday)" Night or morning are redundant on a 24 hour schedule.
When Brennan and Booth are arguing in the lab at the beginning of the episode, a blurred patch under her eyes (possibly placed there to cover dark circles under her eyes) is in the wrong place and briefly blurs her lower eyelids.
At 3344 when Brennan is asking Jesse for the file back from her parents and he is handing it to her, she looks down at the file. The camera then shows the file and it says Matt and Christine Brennan, where it should say Max and Christine Brennan as that is her father's name for the rest of the series.