As far as I know, the quests and Hero Dungeons still count, even with the current dungeon bug.
It's just a matter of exiting out the dungeon at the end. Still got the Hero Bullion and everything.
Only difference from the norm is that we don't stay with the usual party members that we have gathered. There were a certain few that I could play with with no problems at all, but that's few and far between.
Pinkie Pool's archnemesis: Oatmeal.