I've just rescued myself from the ultimate ghost again, completing the second run-through of the game. After being awarded the ultimate ghost hat/mask thing, a screen did say that I can now hire old allies using play coins.
So it seems that the condition to unlock this option is indeed beating the ultimate ghost at the end of Find Mii twice.
In order to get Miis for use in Puzzle Swap, Find Mii and other games in StreetPass Mii Plaza, you must StreetPass with another 3DS owner, which basically means you have to be in wireless range with their system for long enough for the two to realize each others' presence. Once you do this their Mii will appear in the two games.
For Find Mii specifically, a ...
Replaying (from the third time onward) it won't unlock anything new.
If you Street Pass bunch of (the same) people frequently, you can easily get a couple of level 7 characters and some hirelings, and breeze through the game. Or save coins for puzzle pieces.
From this forum thread:
White: fills the area with a bright light. Its only use is on the second to last level, so save them if you can!
Red: attacks ghosts with flames. For the best effect, use against blue ghosts; don't use it against blood ghosts, since it doesn't affect them.
Orange: invigorates heroes. To put it simply, it makes your heroes ...