My Blackberry Playbook's status bar clock no longer responds when clicked. However, it still shows the correct time. Additionally, when I go to the clock app, it takes awhile to load and the times do not match.
A quick solution for this bug is to open the clock app and set the time zone to match your playbook's current time zone.
This bug and its fix were both found in BB10 126.96.36.1998 and earlier.
Normally the clock app and the playbook's time should not get out of sync. It seems as though when this happens, the built-in clock in the status bar no longer works as it should, also producing the problem of not being able to set an alarm. For me, this problem occurred due to an apparent bug (memory leak? buffer overrun?) when playing large mp3 files for a very long time (in my case, it was a 2-hour recording of the ocean overnight for a few days straight -- my neighbourhood is quite noisy).
If anyone at RIM is reading this post, many thanks in advance for finding and fixing this weird bug :) Note that the bug also sometimes seems to affect the ability to network to the playbook itself via wireless or USB, however I haven't found a fix for that.