I don't understand why I can't make a directory on a floppy and copy files to it.
Here is what I did...

[root@daniel dan]# fdformat /dev/fd0
Double-sided, 80 tracks, 18 sec/track. Total capacity 1440 kB.
Formatting ... done
Verifying ... done

[root@daniel dan]# mke2fs /dev/fd0
mke2fs 1.35 (28-Feb-2004)
Filesystem label=
OS type: Linux...
Writing inode tables: done
Writing superblocks and filesystem accounting information: done

[root@daniel dan]# mount -t ext2 /dev/fd0 /mnt/floppy
mount: permission denied

[root@daniel dan]# mkdir -p /mnt/floppy/boot
mkdir: cannot create directory `/mnt/floppy/boot': No medium found

[root@daniel floppy]# umount /mnt/floppy
umount: /mnt/floppy: device is busy
umount: /mnt/floppy: device is busy

[root@daniel mnt]# mount -t ext2 /dev/fd0 /mnt/floppy
mount: permission denied

[root@daniel floppy]# mount
/dev/hda1 on / type ext3 (rw)
none on /proc type proc (rw)
none on /proc/bus/usb type usbfs (rw)
none on /sys type sysfs (rw)
/dev/hda6 on /home type ext3 (rw)
none on /mnt/floppy type supermount (rw,sync,dev=/dev/fd0,fs=ext2:vfat,--,umask=0,iocharset=iso8859-1,codepage=850)

[root@daniel mnt]# cp /boot/grub/stage* /mnt/floppy
cp: cannot stat `/mnt/floppy/stage1': No medium found
cp: cannot stat `/mnt/floppy/stage2': No medium found

I have tried this with two tested good floppies, and I don't understand why I can't copy files to the disk after formatting and creating a file system ???

does "/mnt/floppy" directory exist ?
what are the permissions ?

You can see from the mount command that /mnt/floppy exists
[root@daniel floppy]# mount
/dev/hda1 on / type ext3 (rw)
none on /proc type proc (rw)
none on /proc/bus/usb type usbfs (rw)
none on /sys type sysfs (rw)
/dev/hda6 on /home type ext3 (rw)
none on /mnt/floppy type supermount (rw,sync,dev=/dev/fd0,fs=ext2:vfat,--,umask=0,iocharset=iso8859-1,codepage=850)

The owner is root and the permissions are rwxrwxrwx

Hardware failure perhaps? What about fstab/mtab? I've actually never formatted a floppy in Linux so I dunno.

A hardware failure is not likely. I booted off one of the floppies about 10 times before I formatted it. No problems booting.
I tried an old floppy, and was able to copy files to it - just not the new ones.
I checked permissions on all of them