What makes you think it has to do with WM Center other than the issue, I assume, starting around the same time? If the problem was changes after you synced that might be the case, but since it sounds like you now always have this problems, even when not syncing, that it is more on the PPC side.
I used Quicktasks some time ago and if I recall correctly QT, like most other programs, is using the builtin database for tasks. The first thing I would try, and you have probably done this, is a soft reset. Cures many oddities. After that try narrowing down the issue (although it sounds like a QT issue):
- If you change the date in the native tasks application, or in PI, does it show correctly on the Today screen?
- When you change a date in QT does it reflect correctly in tasks and in PI?
- Can you set a date on a new task in PI or the native tasks application?
You might also want to try uninstalling and reinstalling QT.