I spent a while figuring out what was causing firefox to go up to 99% CPU utilization and Move Media Player was not playing at all.
I found a few other posts through google of people having stability issues with firefox 3.6 in general. But the particular fix for Move Media Player was to upgrade to the latest version of the player (of course). But where do you find it? I was trying to use the Move player to watch General Conference at beta.lds.org/general-conference. As of 4/8/2010 the version they have you download is not the latest one offered by Move.
To get the most up to date one (again, as of 4/8/2010) you can click here to download.