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I experienced the same problem: not being able to see date picker in django admin.
The cause of the problem was a bug in collectstatic command: https://code.djangoproject.com/ticket/15636
I ran collectstatic on Windows, and because of the bug, file /static/admin/js/admin/DateTimeShortcuts.js
became lowercased: datetimeshortcuts.js
So when I deployed it on Linux to be served by Apache, link /static/admin/js/admin/DateTimeShortcuts.js
gave 404 error.
Solution is simple: either migrate to Django 1.4 or run collectstatic on Linux.
Source:stackexchange.com