It has been a long time since I used any of the 1xx series Puppies but from memory I had the same problem. I found that although I was getting lots of error messages when I moved a file. If I tried to open the file in its new location it would open with no problems.
Once I started moving files from the command line I got no more error messages. I don't have a floppy drive so may be wrong here but if you open a terminal in the directory that contains the file (right click > terminal here.)from memory, it has changed in the 2xx series with IceWm. Or click on the rxvt icon and change directories to where your file is. The code should be something like
mv ./"the file you want to move" /dev/fd0/
mv ./"the file you want to move" /mnt/"where you mounted the floppy drive"/
Hope this helps