Dr Sweets' degrees are listed while he is in the courtroom: Undergraduate - psychology degree from the University of Toronto; Masters - degree in abnormal psychology from Temple University; Doctorate - degrees in clinical psychology and behavioral analysis from Columbia University. However, previously in 'The Secret in the Soil', Dr Sweets mentioned that he got his Doctorate of Psychology from the University of Pennsylvania.
During the final scene, Temperance is waiting outside on the court steps alone with extras in the background. The montage plays like Booth exits the courtroom to join her directly outside, but if you watch the middle pillar behind Bones carefully, David Boreanaz's whole right side (minus head) repeatedly juts out as he lies in wait at his mark the whole time, even when the montage starts, so "Booth" doesn't really go directly to Bones.
Bones comments on the method of execution in the state of Maryland. This is irrelevant, since her father is on trial in federal court and not subject to any state's method of execution.
In the lab the Attorney David Barron makes the mistake of saying the state has to prove its case beyond a "shadow of a doubt." The actual burden of proof is beyond a reasonable doubt, as it is all but impossible to prove something beyond a shadow of a doubt.