Butcher changes the license plate on his car from New York (yellow and blue) to Ohio (white and red). When the car pulls away, you can see the New York plate has returned to the car (yellow and blue).
As Annie storms out the front door of her mom's house there is something in her waistband at the rear that causes her sweater hem to rise up in the middle. In the long shot at the door it is missing and the hem lays flat.
Early in the episode Stillwell (Elizabeth Shue), begins quizzing Secretary of Defense Singer (Jim Beaver) about the best selling products from various (and real) defense contractors. He answers that Lockheed Martin's is the Patriot missile, which Stillwell confirms. That missile system is actually built by Raytheon.
During the party at Vought headquarters, an RBC (Royal Bank of Canada) sign is visible out the window.
When Hughie's assault rifle runs out, there are several audible clicks instead of just one. That is not possible since the action is not powered electrically or by some sort of clockwork mechanism but by excess energy from the discharge of the ammunition. So when the gun runs out, there can be at most a single click, and not even that if it has a bolt hold-open feature.