As Troy receives the quantum spanner he's holding it where it's lit up, then in the next shot he's holding it lower, then back up again.
Abed said to Toby, "And you're dressed as the third Inspector, who was famous for trying to strangle the actor who played Constable Dudley, because they were both pursuing Linda McCartney." Linda Eastman See was married to Paul McCartney in 1969 until her death in 1998. This means either the two actors were pursuing a happily married woman, post-1969, or they were pursuing the single Linda Eastman, pre-1969, a fact that would have not escaped Abed.