The tapes will either say "restricted to qualified researchers" or "permission required." You have to get some kind of signature from a lawyer or someone to watch the permission-required ones. If you really want to try, they'll give you the e-mail you need of the person who needs to give you permission.
Yankeefan, as long as none are restricted, and make an appointment, I don't see why you wouldn't be allowed to watch how ever many things you can in the hours it's opened.
"If there was a Mount Rushmore for Broadway scores, "West Side Story" would be front and center. It snaps, it crackles it pops! It surges with a roar, its energy and sheer life undiminished by the years" - NYPost reviewer Elisabeth Vincentelli