Not problems during the fight, problems with the quests themselves not granting credit for victories.
I ran my normal daily route for the pet battles, defeating them all. Went to turn them in, two quests weren't complete, one said I hadn't killed No-No, the other said I hadn't killed Kafi. Went back and killed them again, went to turn in the quests a second time. The Kafi quest was fine, but now I didn't have credit for Gorespine or Ti'un (even though they were marked completed the first time I tried to turn the quest in).
I did have problems today with getting disconnected from the server when starting pet battles, which may have contributed to the issue. But having credit not earn or randomly disappearing is frustrating ><