I'm gonna contribute to this thread with my experience:
Without knowing of the depth of this error, I was playing offline mode multiplayer for an hour or two yesterday. No one used online mode that I can remember. We played fine all day and had been playing fine since last wednesday when I got the game.
All of a sudden, in the middle of a match, I got an "there is an error with the USB memory problem"
(I have a physical copy, but my Smash files are saved on my USB Pendrive thing). I thought it could be a faulty USB drive, so I rebooted, went into Data Management just fine, tried to move the files to the system memory, and in the middle of the transfer, when it says do not turn off, pum, black screen again, error thing.
Scared of having lost everything, I rebooted, went into Smash, and everything was still there. I tried to copy the save file this time instead of moving, same problem.
I turned off the console and haven't tried again. What's different in mine is that I have it on an USB, not on my system, so it's not a system memory issue apparently? I think it's more of a handling data issue. I'm guessing something went wrong with the latest update or something.