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Does anyone knows how to solve the problem with notification lights? 
have you repair your phone with either PCC or SUS?
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http://www.sonymobile.com/gb/tools/update-service/
http://www-support-downloads.sonymobile.com/Software%20Downloads/Update_Service_Setup-2.11.12.5.exe
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
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I've updated the android software to the revision 4.1.B.0.587 and notification light is not working!
There is an unofficial fix, that works very very well....
I'm having the same problem, as I guess everyone else is. What would be useful to know is whether there is an official fix for this on the way?
so far no! But mate that fix works like a charm! I recently pissed off waiting the "official" ICS for my XMP , so I unlocked the bootloader and installed a "generic" 4.1.B.587 then I just applied that fix.
Hey here's how you can fix it lol, apparently if it's charging the text notification light works. Just noticed that one. But it's not too "mobile" like that, any chance of a fix Sony?
No solution until now! 
Will they release some official downgrade at least. GPS isn't working well.