Also, some people have reported success by reinstalling their floppy driver:
Go to Start>Control Panel>System>Hardware>Device Manager>Floppy Disk Drives.. right click>update>install from specifice location>dont search I will choose driver to install>floppy drive> install. After reinstalling floppy drive driver do a full format of your floppy disk and then try copying and pasting some file on the floppy.. it worked for me!
Seems like it's caused by some sort of NT quirk, where it looks for a specific Media descriptor byte, which would basically say "this is a DOS disk" or "this is a mac Disk" (ok,so not really a NT quirk, since it <should> be there) but some manufacturers "preformatted" disks don't have one for whatever reason, so Windows barfs out an error message. Also it seems to cause various issues with formatting those disks as well. This is also why the command prompt has no problems (being able to dir the empty floppy without issues) because command prompt I believe circumvents the particular issue. On that note you might also try formatting the disk from command prompt; from the C: prompt (might not work if it's the active drive) try
Format A:
And follow the various prompts until it formats it (if it can), then see if you can access it via windows explorer.
No idea why resetting the drivers for the floppy would fix it, but apparently it works. By the same token I don't doubt replacing the drive might solve the issue. Even if it didn't at least you'd have a backup drive for the future and you would have eliminated that as the culprit.