Thank you for your post. I apologize for the late reply.
I am unable to replicate this issue; what I did was:
1. Create a new file FileMaker Pro Advanced on Mac OS X 10.6.8.
2. Place a Date field on the Layout and set it to "include icon to show and hide calendar" in the Inspector.
3. Check the third week in the years 2012, 2011, 2010.
The dates appear in my test to be correct -- that is, not duplicated.
Please let me know what I'm doing differently than you.
Nor can I replicate it in Windows XP.
Perhaps it is related to either system settings (DDMMYYYY) or the language version of FileMaker?
What language is shown in your screen shot?