There seem to be various bugs that cause the key issue, which wouldn't be so much an issue if the whole "all enemies must be killed on each stage" rule wasn't so strict.
-I had various enemies glitch out when killed so they'd get up again, be completely inactive but also invincible. Red Templar Shadows, Giants, Hyenas, to name a few.
-Killing wild animals last doesn't seem to bug it out as often anymore in my experience but I've also tried to kill them first now. However, in at least one case a wolf decided to spawn only after we killed everything else, in the previous room no less. Had to restart the wave twice that time.
-Enemies getting stuck outside of the map or something seems to be the worst offender, especially since you can't see them. You can't even be sure what enemy it is.
Over all, if there is no red dot on the minimap, you should be allowed to advance. Or at least give us a way to restart a bugged stage without having the host quit. It practically punishes you for hosting since quitting forfeits all exp. Plus its a gamble for the others since host migration fails quite often.