Is anyone on the forum a good chess player? If so, can you answer if the scene where Dudek plays the whole game himself practically before saying checkmate. Is this realistic? Does he really know the moves Clayton has to make based on Dudek's moves? or do you have any other comments?

I think Dudek made his moves on the assumptions that that is how Clayton would have played the game based on the most logical moves. Clayton, however, could have played the game illogically, but some of his assumptions were correct. You don't want to be down too many pieces to your opponent as this limits what moves you can make and protecting the queen is important since it's the most powerful piece. But, sacrificing the queen is an option if your next move will put you at an advantage.

This is from the Trivia section for the episode on IMDB.Com

The final combination of the chess game played between Dudek and Clayton in the restaurant and finished in Dudek's hotel room was actually played in game Wolthuis-Alexander, Maastricht 1946. Dudek demonstrated the line leading to mate, in the actual game black resigned after the first move of combination, Qxb4. Also, Columbo, when reading from Dudek's notation, says that Black resigned on the 41st move. In the actual game from 1946, the sequence takes place earlier in the game (Black resigned on the 25th move).

Interesting, thanks! I'm 57 and still never learned chess for some reason.