When Kathleen writes "HELP ME" on the chalkboard it is roughly in the center of the board and written somewhat lightly. A few seconds later as the suspect is writing, the words "HELP ME" are now way over to the right, written much darker and is not in the same handwriting.
When Kathleen first realizes Carl is deaf and hands him a pen to write with, as she hands it to him and we are facing her it is top downwards in her hand, in the reverse shot it is top upwards with the cap on, as Carl takes the pen it is top upwards with the cap off.
At 1:23 into the movie, when she is checking keys against file cabinets at the Justice dept., the key won't fit into one of the file cabinets, then the key fits the very next one. This is minor but would not happen. Since the file cabinets are identical, they key would at least FIT the lock (though it wouldn't turn the lock mechanism) unless it were the correct key. For example....all Master Lock keys (of the same sort) will fit the intended item perfectly - it just won't unlock it unless the tumblers match.
The goof item below may give away important plot points.
When Kathleen finds the reported case in which Justice Charles F. Lowell, the District Judge in the 1968 case of United State v. Cook, was implicated, a careful view of the case reveals that the case was a civil case and not a criminal case as it was supposed to be.