Wow this sounds like a hell of a bungled remaster.
It's nothing that can't be mended with a patch. I can't speak for the XB1 version since that seems to be the one with more screentearing / fps drops, but it's not that bad in the PS4 version from what I've played of it. I haven't come across any other issues and Gearbox is working on a fix for both so that should hopefully be out soon.