The UESP says that this location can be cleared. However, I killed everybody in the dungeon as well as everybody on top of it, including the bandit chief. Does anybody know how to clear it? Is it tied to a radiant quest?

Yes, several radiant quests use this location:

• http://www.uesp.net/wiki/Skyrim:Amulet_of_the_Moon: Find the Moon Amulet for http://www.uesp.net/wiki/Skyrim:Kharjo.
  
• http://www.uesp.net/wiki/Skyrim:Arniel%27s_Endeavor: Uncover an ancient Dwemer secret.
  
• http://www.uesp.net/wiki/Skyrim:Retrieval: Journey to a random location to retrieve a fragment of http://www.uesp.net/wiki/Skyrim:Wuuthrad.

and more that have only a small chance of using this spot

You say you want to clear Faldar's Tooth?

http://img229.imagevenue.com/img.php?image=33642_Skyrim_0701_122_44lo.jpg

The thing is, most dungeons that have radiant quests attached to them can be cleared before you even have the quest. Why is this location different?

isn't that that ruine where the bandits let loose their dogs on you , if so i really dislike that ruine and dungon , those archers hurt badly and the bandits inside are tough

but yes i had several quest there , just like i had to go to swindlers den a few times aswell

Yes, I cleared it together with Marcurio. However, one bandit somehow managed to be outside of the ruin right behind a wall for me. Good thing he always heard me without being able to see me, so he talked non-stop and I could easily find him. Maybe a bandit or even a dog managed to escape from your view and is wandering around outside?

I have heard there is actually a second part of the dungeon on top of the waterfall where you fight Falmer.

I think you are referring to http://www.uesp.net/wiki/Skyrim:Stony_Creek_Cave and its unusual path into http://www.uesp.net/wiki/Skyrim:Kagrenzel.

I often approach Faldar's Tooth from the rocky ridge to the southeast. Those bandits usually spot me right away, and generally come in two groups up each side of the fort. A well-placed Frenzy takes the heat off me for a time. The last time I went there, the bandit chief and the wolf that lurks on the stairs of his tower were passing the uppermost window. I could see an occasional flickering, so I took careful aim and shot arrows through the window, and I managed to kill them both!