It's just the AOSP roms mostly. All the TW roms I've tried had very few if any issues. Like i said, AOSP roms are adapted to work on Galaxy S3s, they aren't made for them like touchwiz roms. Touchwiz roms are basically the stock rom modified with tons of added features and root access, that's why they work so well. If you really like the look of AOSP but want everything to work and the functionality of TW try Jelly beans ROM build 15.
Another thing is, are you completely wiping your phone before installing the roms? Or are you just wiping the caches? If you want a clean install and no bugs you should ALWAYS do a full factory reset and wipe cache and dalvik cache before flashing. That eliminates most problems. Now I know it's a pain having to re download your apps and set everything up again but it's worth it.
There are apps like Titanium backup and Carbon that save your apps to your ext SD card and they restore them completely and faster than the play store. I would recommend titanium backup pro. That's what I use and it takes me about 10 minutes to ha e my phone fully setup after wiping and flashing.