I think just about all of them are real (excluding things like the books by Borgin and Benny), I don't remember all the names that Beltik rattled off when he showed up with a box at Beth's.
Modern Chess Openings for example is a very famous chess book that's been reprinted many times.
The book about Paul Morphy, The Pride and Sorrow of Chess is also real but in real life was publish 10 years after the series.
Interesting. Did FIDE ratings even exist in the 1960s? According to Wikipedia, FIDE adopted the Elo system in 1970, but maybe they were using something else earlier than that.
I believe the USSR had a system of third category, second category, 1st, candidate master, etc. analogous to USCF class C, B, A, and Expert players, but without numerical ratings. You moved up to category N-1 by winning a category N tournament or winning a match against a category N player or something along those lines.
I don't know if FIDE did the same thing but I think not. A quick web search finds this saying that the first official FIDE rating list was in 1971. So Beth wouldn't have had a FIDE rating before that.
The 64 cent question is: did you like the book? As mentioned before, I thought it was terrible because of errors like that, but that was ages ago, so I might feel different about it now if I were to re-read it.
Also here to suggest chess.com. It has some amazing tutorials going over everything from how to move the pieces to openings to endgames, etc... They also just came out with a set of chess engines that are meant to mimic Beth's playing throughout the years, essentially allowing you to play against a virtual version of her!