My A600 Floppy stopped recognizing floppies just recently too. Also on my A3000 when I run any games from floppy they seem to skip when there are sound effects, but games run from the hard drive appear to work fine so far. I don't have a lot of games, so I cannot make a full result on that as only 3 of my games are HD installable.
-edit- Sorry made some changes to make my post easier to read.
Nathan