There should be a Table of Comets in that pile of books for Spock to ignore.
I'm really digging that Mr. Scott's Guide Food Slot. I don't think I've seen it modeled before.
I assumed the theater was a live performance space (we saw one in TOS in "The Conscience of the King" that seemed to be a purpose-built (and much larger than the chapel from "Balance of Terror." IIRC, the theatre was the engineering set, and the chapel was the briefing room. It does make sense for them to be the same space.