Give a selection of your friends who have oauthed (requires persistence, see other issue), and on selection, show the area they've explored as red overlays. Not sure whether to include areas that fall outside of your explore regions or not. Will have to play with it.
Another option (HT: Kushal): show areas where you haven't been but your friends have been with lighter opacity.
Figure out a way to make it competitive (HT: Alex - "battle mode").
Added two views here:
vs. mode - single opponent - show your territory, their territory, and the overlap territory, and give scores for each
multiplayer mode - up to 5 opponents - show all territory, with the owner of each grid being the one who checked in their the most