Revealing mistake: When Bob and Joyce have lunch, Bob pops open a can of soda (which is period appropriate). The scene cuts to Joyce, then back to Bob. It is clear from how he is holding the can, and how he pretends to drink from it, that his newly opened soda is actually empty.
Revealing mistake: Right after the scene in Wallace's office where the DHS tries to shut down Hayes' investigation, the scene shifts to a montage. Towards the end of it there's a loop: in the bottom left corner you can see someone on a scooter appear from the left, only to disappear a second later and reappear from where they'd come the first time. (00:20:00)
Revealing mistake: When the sniper is aiming at Swagger and the soldier through the window, a woman walks in and notices him. He shoots her and she falls. The problem is, he shoots at nothing. She simply turns her head and acts like she got hit. There's no indication a bullet even hit her.