I've noticed a strange behaviour in my living application and started striping down my page.
The datepicker does not work (it does nothing, no popup - see error trace below).
I could nail it down to the tab widget (at least it seems to produce the error, I don't know if the same happens with other widgets).
So to test: Create e page, insert a date widget, test it. Then insert a Tab widget, test it again.
It doesn't care where you place your date widget.
This is what I get in the console: