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Today I kept my phone for charging as usual when the battery level was 20%.
I checked it now and it was still just 70% and it has been more than 3 hrs now.
Immediately I was shocked to find that the Camera LED light was constantly ON!!! 
I immediately opened Torch app but it did nothing nor it was running in background.
I tried to access camera app even that wasnt running in bg and it threw some error that "Error camera not available".
So for 3hrs my camera light was ON. 
I fear if that has done some damage to the light itself. 
Worst, Since yesterday I havent access camera app or anything relating to camera or the torch then how has the Light got tuned ON AUTOMATICALLY???
Now its like a panic type situation for me and obviously for anybody in this situation.
I'm now very furious upon this. Now does that mean we should constantly keep observing our Z3 while charging for a good 3 hrs or so??
That's clearly an app acting up, repair your phone with PCC and do NOT install any other app for 3 or 4 hours and check again
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Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355