Character mistake: When Ellerby tells Sullivan "Some people don't trust a guy with an immaculate record. I do. I have an immaculate record." Really? An immaculate record even after you punch they guy's lights out for not installing the cameras right? He's a captain, had a long career, if he punches a guy for that, certainly he's had other complaints before too.
Suggested correction: This is too presumptuous to be a valid mistake. We know practically nothing of his history, so it can't be definitively said he's had complaints about him before. The assault he committed over the failed sting could very well be his first infraction, and if it is still being investigated, it won't appear on his record yet.
It's also possible that people simply don't complain about outbursts like that in an environment with inter agency cooperation and high tensions.
Character mistake: During the funeral at the end before the 21 gun salute, the NCOIC called for "half left face", that would cause everyone to get shot in the face.