I still have the golden claw from the beginning of the game, I killed the bandit holding the claw as soon as he was free and now it says I still have to find him although he's dead and the quest was finished about 20 hours ago.
The quest doesn't end with you killing the bandit...
Perhaps I should be more clear,
Spoiler
I kill the bandit, use the claw, get the word, talk to the jarl, defeat the first dragon, climb the mountain, talk to Agerier, learn the whirlwind shouts, jurgens horn, etc. . .and the quest menu still says I need to find the bandit