Do ash piles/ghostly remains/etc still remain indefinitely?
Ash Piles used to remain indefinitely (was not properly cleaned up by the game), but is fixed as of patch version 1.4. Certain ash piles from resurrected NPCs also used to remain indefinitely, but this is fixed as of patch version 1.9. Nirnroot lighting or glow objects also used to be not properly cleaned up by the game, but is now fixed as of patch version 1.6. Related patch change logs:
Fixed issue with ash piles not cleaning up properly (v1.4)
Fixed issue with nirnroot lighting not properly cleaning up (v1.6)
Fixed rare issue with certain ash piles left from resurrected NPCs not clearing properly (v1.9)
However, Ghostly Remains, Ice Piles, Wisp Cores, and items dropped in the ground (even weapons and shields by NPCs), are currently not fixed by an official patch, and will permanently remain (contributing to save game bloating and game lag). These bugs are fixed by the Unofficial Skyrim Patch (PC) / (Xbox One) / (PS4). Related fixes, from the USKP patch list:
Ghostly Remains, Ice Piles and Wisp Cores will no longer permanently remain and bloat the save file (they will either disappear on exit of the cell or when the cell resets).
NPCs will no longer drop weapons or shields as separate objects, as these are never cleaned up which greatly adds to save bloating and litters the gameworld (the items will still appear to be dropped, but will access the corpse's inventory to be taken and be cleaned up with the corpse if left)