I went and recreated th-cam.com/video/4VTzH6phgPw/w-d-xo.html using a GV-USB2 capture device and a real SNES, and I included the full process of me setting everything up to cause the error.
It's really easy to do! I saw a suggestion to do it with a custom stamp which I did here, but you can also do it with a premade stamp (like the one of Mario's head), the spray tool or any other method of making something that looks very messy. Just keep in mind that you do need to do this to both the main canvas *and* the animation frames.
This error happens because Mario Paint's cartridge includes 32 KiB of save memory, but that's only enough for the main canvas or the animation frames but not both. The game solves this with compression, and if the data is random enough then it'll still be too big to fit after compression.
If you're not familiar with Mario Paint you might notice that Mario Maker actually references it quite a bit.
2:20 Save animation
3:02 Error