"Kill the dragon" quest - dragon didn't appear in the world after I gave crystals to oldman.
"Kill guardian statues" - killed statues, chose to not break the walls. A message appeared like "Now it's time to explore the dungeon", but quest still active with same task, nothing new appeared, questgiving location doesn't react.
"Riders compound" - killed first set of enemies, used "escaped" on second wave, then killed them on world map - quest disappeared.
"Great earth elemental" or whatever, don't remember name - a green area. Other factions seem to have killed all elementals that roamed the region, leaving to me unguarded lairs and a crystal that must be gathered with monument. Still the quest appeared to "Kill Whathisname" to claim his lands.

All in all, I think in some (most) cases if you decline to enter a dungeon (to enter it with another party for example), the location should change its text and stay on map. It kind of makes little sense to lose a dungeon or arena forever if a weak champion stumbles into it.
Same should be for Escape spell, or even defeat (remember in MoM - you could reenter towers, nodes etc)