Continuity mistake: When Kathleen goes to talk to Carl, her client, while he's in restraints she writes "You're deaf, aren't you!" on a legal pad then sits on his bed. She's holding her Sharpie in her hand, cap end up. When the perspective changes to Carl's, the Sharpie is cap end down. The shots go back and forth another time the same way.
Continuity mistake: Kathleen Riley and Carl Anderson are in a room with a blackboard. As they write questions and answers on the board, the writing changes several times between shots.
Audio problem: Toward the beginning of the movie, Kathleen is in her home going through files. She comes across something (likely the fact that Carl is deaf), and says to herself out loud, "Can't they read?" But her lips do not match what is said.
Other mistake: When Eddie Sanger is saving Kathleen Riley from "Michael", he gets slashed in the chest, through his leather jacket and sweater. When they meet up the next day, he is wearing the same leather jacket. Although the front is not shown, it is the same type and colour and obviously same jacket. He doesn't seem to be the type who would wear a slashed and likely bloody leather jacket.
Suggested correction: He gets cut through the sweater only. The jacket was unzipped and does not get damaged, therefore the fact that he is wearing it a few days later is a reasonable decision.
Revealing mistake: Carl is supposed to be deaf. However a few times in the early interrogation room with the officers and Kathleen, or just Kathleen alone (during questioning) his body movements and reactions reflect otherwise. Unless he is just keenly aware of his immediate surroundings.
Suggested correction: Looking at the scene that I at least think you were talking about, or any other scene for that matter, Liam Neeson does nothing that I would not expect a deaf person to do. It's not like he reacted to a loud sound that a deaf person shouldn't be able to hear. I see nothing out of the ordinary. Perhaps if you use a specific example.
Revealing mistake: The homeless man attacks Kathleen and she screams. But it isn't until 5 minutes later that Sanger comes to her rescue, when he only left moments ago.
Other mistake: When the Assistant DA Stella questions Sanger about his views on capital punishment, Kathleen objects the query as improper for the hearing, and asks the justice to disregard, which he does. But then he proceeds the disregarded query to Sanger again.