Pass: If a player discards a Common Item while in an Other World, return this card to the box. Each player gains 2 Clue tokens.

We play it that the Common Item is discarded only in the Other World Encounters phase, but some friends discard the item in any phase (Upkeep, Movement, Other World Encounters and even Mythos). Which one is right?

From the updated FAQ draft:

Q: For the rumor Return to the Old Ways, is
discarding a common Item to pass the rumor subject
to being discarded on a roll of 1 or 2, thereby not
passing the rumor?
A: No.

Q: Do common items discarded for
other purposes, including their own uses, count for
passing the rumor?
A: No.

Looks like to pass the rumor, you, at any time while you're in the Other World, pick a common item you possess and voluntarily discard it. My guess is that you still have to fully resolve encounters, battles, and Mythos cards (and so can't pass the rumor in the middle of these events), but can pass it any other time.