The footage of the Gotham City World's Fair that opens the show is actually of the New York World's Fair of 1964-1965. The building identified on screen as "Republic of Moldavia" was the Thailand Pavilion at the Fair.
Frank Gorshin created the green business suit and hat with the question marks for the Riddler since he hated the green skintight jumpsuit costume from the comic books. Although that alternate costume was ignored in the comics for decades, the popular TV series, Batman: The Animated Series (1992), featured the supervillain in a more restrained version of that costume, obviously inspired by Gorshin's design, and the character has typically worn that style in the comic books ever since. Jim Carrey's Riddler also wore both styles of costume onscreen.
While filming the scene in which the Riddler attempts to steal the Batmobile, Burt Ward suffered severe burns when sparks from the dashboard's pyrotechnics display ignited his costume.
The republic of Moldavia, an ancient kingdom in Europe, actually existed as such under Soviet rule. Today it is the nation of Moldova. It is particularly known for its fine wines.
Based on a comic book story published in Batman #171.