Even with Broken Token, my box is getting pretty full.

Besides the per-scenario encounter sets, are there any encounter sets that are only used once? (i.e. that you can stash somewhere else once you've played particular scenarios)?

Not that I can think of. And there have been a few cases of scenarios using scenario specific cards from the core set. Threads of Fate in The Forgotten Age uses locations from the Midnight Masks scenario from Night Of The Zealot. I wouldn't be surprised if some of those locations get re-used again for the next campaign since it is Arkham-centered. Might be partially how they have the space to have the prologue scenario on top of the normal two.

Besides the scenario sets? No.

The "Cult of Umordoth" encounter set is only used in "The Midnight Masks."

The "Pillars of Judgment" and "K'n-yan" encounter sets are only used in "The Heart of the Elders."

1 hour ago, rsdockery said:

The "Cult of Umordoth" encounter set is only used in "The Midnight Masks."

And "The Devourer Below" if you don't take care of all of them.

13 hours ago, Duciris said:

And "The Devourer Below" if you don't take care of all of them.

And it could be reused later, since it's from the Core Set.