I have been playing Skyrim for many hours, not sure on how many. I've had 3 different characters, each a different race (Kajhit, Argonian, Nord) and have similar glitches in each. I have either cleared an area prior to a quest, or cleared an area because of another quest, and so cannot complete a quest because of this. Currently, I'm searching for the last Hircine Totem. I'm on a quest between the 2nd and 3rd totem quests, and asked to clear a grove. An arrow appears, and shows up in the air above my characters head. There are no animals or anything (including deer, elk, rabbit, fox) in the area to kill. I don't recall the name, but it's the one where a hunter is in an overhang with a chest and animal pelts in the wooden alcove that also holds the chickens. I believe when I first came across it, there were 2 sabre cats in the overhang with the dead hunter. These glitches are still there and I don't have a previous save prior to clearing this grove. Is Bethesda looking into a way to fix these glitches that are caused to previously clearing an area and not being able to finish a mission because of it?
SIMILAR GLITCHES: The bard who asked me to find a drum was killed either by a Vampire or during the Battle of Solitude. I cannot find his body anywhere, and an arrow won't appear when I turn the option on. I am stuck with the drum and cannot remove it from my inventory. I was told, if I can find his body, that I can "give" it to him and complete the mission. No body, no finishing the mission.
Markart: Stealing the Dibella statue for Degaine- I talked to the innkeeper, and the quest wasn't brought up. Talked to Degaine, activated the misc quest, and finished it. Talked to the Innkeeper, and reactivated the "Talk to Degaine" misc. quest. He won't continue the quest since I'd already completed it, so can't get rid of the quest.
Thieve's Guild/Jarl Bounty: Clear out the cave with the wannabe Thieves Guild- I cleared it out with the Thieve's Guild and was reactivated by a Jarl Bounty. I can kill all the others, but the leader isn't there. The arrow (from above) shows in the room below and (from the room) appears in the ceiling. Tried a few more times and it changes from saying the leader is IN THE FLOOR/CEILING, to being in the floor of the room he occupies.
There are a few others, but it's pretty much the same thing over and over in the glitches. You get the idea from these examples.
Bethesda stopped all work on Skyrim two years ago i'm afraid the only new bug fixes are on the PC with the unofficial patches, Sabre Cat's are missing the coding that makes them respawn so if you cleared them out of a cave once they will never respawn unfortunately (the Unofficial Skyrim Patch fixes it).
Animal Extermination is radiant if you reload before getting that quest then do a few different quest you might get a different location when you ask again (only a might though). On the PC you could try to force the quest complete with the command -