Are you one of the players that items are not been added to your inventory or not been considered to complete the quest?
Another problem several people where asking as to do with items in the Quest Inn. Below there is the answer for the Pieces of Map. You are collecting them but they don't count for the quest or simply they are not been added to your inventory. Thanks to all that reported this problem before.
In this case, Zynga says that they will fix it in 72 hours.
If you are having troubles, go to the support page, check if your problem is there and click "Please Fix IT" in order to increase its priority in fixing it. No matter what, your game problems should be reported to Zynga. Only confirm before that you can't solve it and what is the information you should send to Zynga. A good way of doing this is posting your problem in the Facebook Page or Group. There is always another player able to help you.
Another problem several people where asking as to do with items in the Quest Inn. Below there is the answer for the Pieces of Map:
Players unable to complete Royal Inn Quest 11 of 13 due to Item Cap
Last Update: 1/29/2011
Since 1/27, players have reported not being able to complete Royal Inn Quest 11/13 because they had 3 or more Pieces of Map before beginning the Quest.
Status: This is a top priority for us and will be addressed early this week (within 72 Hours).
Link to bug report thread: Here