It's happening again, I have the items, says I don't, stuck till I shut off the browser and loggin again. Annoying.
Same here. Just did Quentin's quest twice(same items). items gone and won't let me go to the next quest. Says I don't have the items, then goes to a white page when I try submitting the items.
Third time it worked after completing other quest.
So this has happened to me a bunch. IT MAY have something to do with how fast I am clicking, like I've got no patience what so ever. But if other people are experiencing this too then maybe it isn't just me.
I buy both items for the quest making sure it tells me I have purchased them. Go to click finish quest. Get an error saying I am missing one or both items. Go back to the last page, it says I'm not on a quest.
Back to last page again and a hard refresh will shoot me back to the Start a Quest page saying I did actually complete the quest 4/15 etc... I am being compensated for the quests as far as I can tell, at least the wizard still gave me tokens. But it is a bit annoying to have to play the refresh game to be able to keep questing.
Here are some screen shots to better illustrate my point:

and 's workarounds do both work, and Cheshire's explanation is indeed what's going on. You can also do URL tricks where you remove the /whatever after the questname and refresh: this sends you back to the first page of the quest.
You can avoid this problem by doing your quests more slowly and evenly.
It's been this way for awhile, so it's probably not fixable.