Certain cards and/or spells in Arkham Horror allows/forces you to return prematurely to Arkham from other worlds (e.g. 'Find Gate'). Can you then close the gate, or do you have to do the whole thing over again?

There is an official FAQ about this... they say: " In general, whenever you “return to Arkham,” you reappear at a gate that leads to the Other World you were in and gain an “explored” marker". so you can seal the gate in the next encounter phase.

Generally, if a card says "return to Arkham", you are treated as if you had explored the Other World enough to be able to close/seal the gate just as if you had done it normally by having encounters in both areas. If a card says something like "move to the Black Cave" however, like the one where you have to roll to see which of the divergent tunnels you head down, then you are not so lucky.

Excellent. Thanks very much!