I recently began seeing problems with battery drain on my Note 3. It's running stock KitKat and is unrooted. When I looked in settings and the 'power' page, I noticed the battery drain was highest with 'mediaserver'.
After a number of searches on forums and lots of suggestions that didn't work for me, I figured out how to prevent mediaserver doing this. This is a manual fix and irritating as an Android bug, but so far the only thing I've found that works consistently.
The only apps I use for playing any kind of media stored on my mobile are MX Player and Poweramp. Two popular and fairly standard apps most people have and use. What I found was that whenever I'd played a movie or TV show with MX Player or audiobook with Poweramp and paused it (pausing playback is the key to this), the battery drain began. If the media file is paused, it seems mediaserver leaves itself open and using resources presumably to enable rapid resuming of playback from within the app you were using.
So, if I pause something and am not likely to resume playback for a while, I go into Settings - General - Application manager, and find MX Player (or whatever app I last used to play media). In the App info page I select 'Force stop'. That's it! Problem solved! No more mediaserver battery drain.
Until this long term bug is patched, this is a solution that works well for me. I hope someone else finds use for it too.
P.S. Although this definitely works with MX Player, I haven't yet monitored battery life fully with Poweramp too. I'm just assuming the mediaserver is running with Poweramp too.