The main goof made during the French restaurant scene between Columbo and Clayton is when Columbo comments that he was "kept awake last night" because of the question of why did Thomlin Dudek not take his chess set with him. The scene was supposed to take place on the same day as the supposed accident. The previous night, it had not happened yet.
"The Most Dangerous Match" was an excellent episode, even if Thomlin Dudek did not list the names of the players in the recorded French restaurant game in his notebook.
This doesn't qualify as a mistake, but I've always though Clayton took a chance in one area. He dictated that note full of very general apologies, but he also told Dudek that it was to a woman, about ending a romance. So it always seems to me that Dudek could have worked in some reference to that, showing that the note had nothing to do with the chess match. So that would have made things bad for Clayton from the start.