Visible crew/equipment: When Ethan is trying to get into the building for his interview you can see the lapel mic on his back. He leaves the building, runs back in through another door, a guard flips him and you see it on his back.
Continuity mistake: In the scene just following the opening physics exam we see the guys sitting smoking a joint and talking to Philip, the one they are paying to write the test. In one shot Sam hands Philip the joint and Philip says something about them doing better on tests if they stopped smoking pot. The shot changes to Sam speaking and he still has the joint. The shot changes to Philip and he is just handing the joint back to Sam.
Continuity mistake: At the end of the first exam when "cool Ethan" goes to look for dropped hair and sees Dave's name and number, in the scene following, you can see there is a pile of hair, as opposed to a single one. I imagine it was placed there by props so Jason Schwartz (Ethan) would have no problem picking it up. (00:11:25)