Stevesvp is correct: it's an Actiontec router issue. And it's not just with Mac OS X: the same problem happens with other devices that have nothing to do with Apple (TiVo, Samsung TVs, etc). I'm not sure why 10.4 works, maybe it's using an older way of accessing Bonjour (the Bonjour protocol has been undergoing changes to try to address complaints from large network admins about chattiness), but it's not Apple's fault. And this problem doesn't happen with any other router than Actiontec.
The Disabling IGMP Proxy via the Actiontec's "Advanced -> IGMP Proxy" menu works fine and solves the problem.
One complication is that the new Rev I of the Actiontec router removed the link to the IGMP page from the Advanced menu. If you have that Rev, however, you can still get to the IGMP Proxy menu via a deep link discovered by user BigDaddy on DSLReports. Just loging to your router as normal, then use this link, which will take you directly to the now-hidden IGMP Proxy config page:
192.168.1.1/index.cgi?active_page=6059
I can confirm that this works on my Rev I router.