android.process.media appears to be, as the name suggests, "Media Storage" crashing. Clearing "Media Storage" cache doesn't work when another app is causing it to crash -- and this app is almost always "Download Manager". Clearing the cache of both apps fixes it:
- Settings -> Application Manager -> All apps.
- Find "Download manager", and select "clear cache".
- Find "Media Storage", and select "clear cache".
Some odd websites suggest disabling "Media Storage". Well of course it will get rid of the errors... But you won't even be able to access the pictures you took from the Samsung "Gallery" app, or even take photos or screenshots.
Source: I had this problem again with my good old Note 3. Writing this to help others because most websites don't help much.