The consensus on this is that it is pure luck whether old smart covers work or not. It depends on the polarity of the magnet that was inserted into the case when it was manufactured. New covers have a consistent polarity which matches the iPad3. Old covers may or may not. It's a 50/50 chance. My old Smart Cover for the iPad2 works fine on my 3. Other folks cases dont. It's a very weird situation.
If you are feeling brave (and can't use the case for anything else), you can pry open the case, flip the magnet, and glue it back together again. Then it should work.