I've been experiencing the same problem.
I've found that it sometimes works if I go into full-screen mode first, and then plug in the HDMI cable. It all goes black for a few seconds, but then the video shows up in fullscreen on my TV.
As for the freezes, usually I have to close the browser, kill it, open it (and sometimes repeat several times before I can even navigate back to the page), then fire up the video again. But I've found that sometimes I can just power off the device (ie tab power button to turn off display), then turn it back on after a couple seconds, and video starts playing again correctly.
What a pain, though. Never had these problems with Honeycomb.