In some languages (update: languages with lang string indicating first day of week = Monday) date picker popup contains too many table cells with names of week days - see screenshots.
Number of columns in calendar is okay (seven), but duplicated week days unnecessarily enlarge the control, that looks broken in result.
I found the problem specifically when editing due dates for Assignment, but wherever the date picker is used, the problem repeats consistently.

In default English locale everything is okay, so this may have been unnoticed for a while. I've checked some language packs using http://demo.moodle.net/ and the problem can be reproduced in number of them.

Tested:

• en - OK
• fr - BROKEN
• it - OK
• ja - OK
• nl - OK
• pl - BROKEN
• cs - BROKEN

On last Thursday when I was looking for clues, at least in one language (can't remember which one, sorry) the popup looked good, but it contained English names of week days.
So I suspect the problem might be related to language packs, but I was unable to confirm that. The date picker is full JavaScript YUI and I was looking in PHP code that could invoke it or prepare input data, however without success.

update: please also see MDL-49488 - when locale was not correctly set calendar threw a JS error (that issue is closed as deferred to this one)