I came across a random corpse with said note on the body which launched a Radiant quest upon opening. I was sent to "Crossroads Watchtower" (a location that doesn't appear to exist, though the map marker actually led me to Falkreath Watchtower). I was supposed to retrieve an axe from a necromancer.

I found the location (again Falkreath Watchtower, not "Crossroads Watchtower") and killed the necromancer, and by extension, his thrall. Note that the thrall had the object equipped, whereas these Radiant quests typically have the quest item in a chest.

The thrall turned to ash upon the necromancer's death and the axe was not in her inventory, rather just laying on the ground. I was able to pick it up, however doing so did not mark the quest complete.

I can drop the item, sell the item (the quest marker now points to the store-owners chest below the floor in the cell), etc, however nothing I seem to do will update the quest.

Here's the list of potential issues causing the issues:

1) actual location doesn't match the name of the location assigned by Radiant AI
2) quest item not in chest
3) quest item not equipped by target assigned via Radiant AI
4) quest item not in inventory of last user

In the mean time, if anyone knows a cheat code that I can use to mark the quest complete, the help would be greatly appreciated. Thanks for reading.