When Brian goes to Eli's flat, he doesn't shut the door behind him. Moments later you can hear the FBI agents pounding on the door and saying "Open up!"
During his off the books meeting with Brian Finch, Senator Morra's eyes change color due to the discontinuity of the blue scale editing. In one cut the enhanced blue color fades out to the natural blue-gray of Bradley Cooper's eyes.
When Brian is talking to Rebecca on the phone after he got shot, Rebecca writes on a yellow legal pad the word "SHOT" and shows it to her partner through the glass window. The legal pad she writes on is not the same one she holds up to the window. When writing, she connects the O and the T, but when held up to the window, the paper distinctly shows the letters written separately.
When Rebecca is on the phone with Brian and talking about his gunshot wound, she asks him whether the bullet is "in your leg still," even though Brian did not tell her where he had been shot.