This is a big reason why backing up your physical media is nice, because you can get around issues like this with no problem. Whether it putting everything on a Plex server or ripping your media to a hard drive, you wont have to worry about disc transition problems if you take that route. It definitely not for everybody, largely because it adds an extra cost on top of buying the discs in the first place, but if you want to make sure you get the best experience possible without skipping, then it...
