Unhappy [Q] SGS3 with Android 4.1.2 "sort of" freezes randomly

Hi,

Since a week or so now, my Samsung Galaxy S3 with a rooted Android 4.1.2 "sort of" freezes randomly. And with "sort of" I mean that animations and such (can) keep running, it just doesn't respond to any kind of imput anymore. I had it freeze on a youtube video, but the video kept playing till it was done (but it didn't continue like it would afterwards, so the process definitely froze too).
I have no clue what sets it off. I've had it freeze while using navigation, while browsing, while typing, while taking a photo, while turning the screen off (it will just stay on forever), anything. Sometimes it freezes 5 times in 5 minutes, sometimes it freezes only once a day. In all cases, the only way to get it back to life is by taking the battery out and putting it back. Waiting doesn't do anything.
I thought it might be a memory card problem, but I unmounted the card and got the problem again just now.

I figured I'd download an app that writes logfiles to see what is happening, but all those programs don't work anymore with the current version, due to that the programs only have access to their own logs now.

Does anyone have a clue to what might cause this, or a way to troubleshoot further and try and find the solution?

Thanks!