Factual error: Lobbyists (or any other private citizen) are not subject to Senate Ethics rules. Only actual senators are. Sloane committed no offence in organising an expensive vacation for a senator. The senator did by accepting it, though.
Factual error: The 5th Amendment to the Constitution simply states that "No person... shall be compelled in any criminal case to be a witness against himself." There is no actual or implied provision that means once you have answered a question, you can't plead the 5th on any subsequent questions, as the movie depicts.