Other mistake: In the hotel room shootout, bullets are being fired through the wall easily and tearing up the place as you'd expect. Frank then dives through the damaged wall and they shoot at each other with Frank behind a cupboard and Pilgrim behind an internal wall. But bullets empties into both of these bits of flimsy cover leave the men behind them miraculously unscathed.
Revealing mistake: The first time we see the raid on the senator's room, 2 security guards are shot in the head. The blood spray from the second one emerges a fraction of a second before the gun fires. The second time the raid is played out, everything happens exactly the same way, but this time the spray matches the gunshot. (00:11:10)
Character mistake: When Frank is starting to show Amy how to take the gun from him he removes the magazine and makes the statement "clip empty" - any Marine, certainly one as well trained as him would never refer to that as a "clip" - it is a magazine. A "clip" is a device intended to help rapidly load ammunition into a magazine.
Other mistake: During the shootout in the hotel rooms, Pilgrim and Frank are shooting a lot at each other through the wall, with multiple holes appearing as expected. They then swap rooms (Pilgrim going through the adjoining door, Frank down the corridor), and we see Frank shooting at Pilgrim from the opposite angle. Problem is we see bullet holes appearing in the undamaged wall behind Pilgrim - given that room was just being riddled with bullets there should already be plenty of bullet holes in that far wall.
Continuity mistake: The flashback to Ahmad Zubair being tortured is different than the video Frank watches in the previous episode, Two Dead Men. For example, in the video, after the masked man stops choking Zubair, he keeps talking in Pashto. But in the flashback, his hands are around Zubair's neck the entire time and then speaks English before having him shot.