Thanks for writing these.

The patch looks good to me (caveat: I only have a passing familiarity with asyncore).  A couple of English nits:

   A server which listen on an address and dispatches the 

should be 'listens'

    # EADDRINUSE indicates the socket was correctly binded

should be 'bound'

And one style nit: I'd perfer to see a 'BaseTestAPI' that has no base class, and two TestCase subclasses that use BaseTestAPI as a mixin, one for use_poll=True and one for use_poll=False.  It's not a big deal, though; what you have is fine if you don't feel like changing it.

As discussed on #python-dev, it would be best to make a branch in which to apply this so you can run it on all the buildbots.  This is especially true since you have one test your comments indicate you are pretty sure is not going to work on all platforms, and it would be nice to add skips for those platforms before checking it in to trunk.