Last night, on a whim, I asked my Toshiba HD-A1 HD DVD Player to see if there was a firmware update available, and there was, and it proceeded to download it from the web. I took a dinner [that's a unit of time] to do it. Due to the new baby I regret to announce I have only manage to watch one HD DVD movie since I got the player, and last night I had all of five minutes to try the new firmware. All I can tell you is the machine turns on quicker. Those in the know say that the HDMI connectivity issues are fixed, general stability is improved, and many users are saying the black levels over HDMI are also fixed (though not everyone). For the official info see the Toshiba site (its an annoying Flash-site so go here then click on Support then Firmware Update 1.2). For the AVSForum view see this thread, but skip past the poor folks who can't get a simple ethernet connection set up.
Firmware upgrades can't get much simpler than this. Its like Windows Update, but on your DVD player (though lacking the "automatically get me the latest updates at 4am" option). Sad folks without a broadband connection can ask Toshiba to send them a disc with the new firmware: how quaint.
If I get the chance I will attempt to play with the new firmware soon and post my findings here.