After attempting to throw a vat of sodium hydroxide (lye) down from a shelf onto the Beggar Man Trevor climbs down the shelves and slips, landing in the solution of lye. With the way he landed the bottom of his pants would be partly dissolved and his hands would have severe chemical burns and be in extreme pain. Yet he seems perfectly fine in the next scene.
When Doggett is telling Scully about the prints found in Quinton's room, the camera angle switches to a shot from behind him where his jaw movements don't match up to what he's saying.
In the opening scene when the first cab pulls up at the airport and the camera closes in, it's shadow can be seen on the hood of an adjacent cab.
John Doggett states that one victim's death certificate, filed in India, was written in Farsi. Farsi (or Dari in Afghanistan) is a language which is primarily spoken in Iran, Afghanistan and Central Asia. There are relatively few speakers in India and it certainly wouldn't be used for government documents such as death certificates.
Near the end of the episode, when the police arrive at the house, it is the Washington, D.C. Metropolitan Police Department shown responding. However, that would be out of their jurisdiction as the scene takes place in Prince George's County. It would make more sense to show the Prince George's County Police Department responding there.
When the Beggar has Quinton cornered in the classroom, just as Scully enters with the Principal the Boom Mic becomes visible just left from the center of the shot.
Agent Doggett mispronounces Ebola as "Eboli".