When Parker arrives in Hardison's apartment, his CIA file is open on the floor. When she picks up the file, it's closed and she reopens it.
When the guard uses the stun gun on Eliot, Eliot first grabs the front end of the stun gun. When the view changes, he is holding the guards hand.
When Parker is volunteering in the Psychology Department, shocking a patient is described as "negative reinforcement." However, the practice of using painful or unpleasant stimuli in psychology is called "punishment." These two terms are often confused, but are quite distinct in the psych literature. In any event, the particular experiment shown is considered unethical and would never be sanctioned in an university.
Nate's lecture about the Prisoner's Dilemma is wrong. Game theory research suggests that, in the scenario Nate posits, it is in the subject's best interest not to give up his accomplice. This could be an intentional "character error" or a mistake on the part of the writers.
When Hardison is playing video games with a cigar in his mouth, the cigar is unlit.
During the episode "reveal" the door signage on the room used for the police interrogation is misspelt as PYSCHOLOGY TEST LAB 1B.