Of the prospect of Jane Molloy leaving his firm for Sloane, Pat Connors tells her: "I could care less." This is a common mistake. If he means to convey that it does not affect him in the slightest, he should say that he couldn't care less. Saying that he could, in fact, care less, denotes a degree of caring that is not equal to zero. But this may be a deliberate affectation by the screenwriter, precisely because it is a common mistake.
(45:55) At Peterson Wyatt, where all lobbyists are now gathered, Elizabeth asks for "arguments and rebuttals". Alex then starts writing on a board the first four letters of "National Register". The camera switches to Elizabeth speaking, then, when camera returns to Alex, the size and position of the writing are clearly different : bigger and more to the left.
The goof item below may give away important plot points.
During the hearing where she testified, Miss Sloane gives the assembled crowd the IP address for a website containing a video that turns the table on her accusers. The last number of that address is 449. The four numbers that make up an IP address are one-byte values, so they can't go beyond 255.
At the end of the movie Miss Sloane is incarcerated at the Federal Correctional Institution in Anderson, MD. This place is fictitious. There is only one Federal Correctional Institution in Maryland and it is in Cumberland and is male only. The movie may be alluding to the prison in Alderson, but this is in West Virginia and is a Federal Correctional Camp, not an Institution.