One thing that's always confused me (and maybe it's meant to be a little unclear) is Emmett Clayton's nationality, which isn't mentioned any more than Tomlin Dudek's (even though you're pretty much meant to assume Dudek is Russian). Clayton is played by very British-sounding Laurence Harvey (yes, I know he was originally from Eastern Europe), but there's that scene where that one American reporter seems in awe of Dudek, and Clayton kids him about not being very patriotic. So that kind of suggests that Clayton himself is meant to be an American. So THE MOST DANGEROUS MATCH is kind of confusing when it comes to nationalities, maybe deliberately.

They have an American flag and a Soviet flag in the chess room when Clayton is "waiting" for Dudek to appear for the match.

I guess I never noticed.