Well this is a long shot, but does the sff file have .sff part in its filename?

Did you try step 4?

Ok let's walk though all the simple stuff.

1. Stages in stages folder.
2. Imputed into select.def. Now if your stage name has spaces in it and you attach to a player in select.def then you would have a problem.
3. Open stages.def file and make sure that it has the .sff listed and don't have any crazy pathway like stages/sff/mystage/whaterstage.def
4.When you get an error for a specific stage remove said stage re download mugen put stage in that mugen and run the game. Just see if it works and get back to me.

Edit: Try Hisui's idea first sounds like a good one.

Try opening the stage in Fighter Factory and saving it again as an sff file.

Try this. Right click on any .sff and def and open with notepad and set notepad as the default program. The only thing is this should have nothing to do with mugen so in a way I'm just throwing a guess out but maybe if paint is set as default then may be when the file paint somehow is messing it up. Let me know if this guess has helped in mean time I'll try to think of something else.