Just bought a Samsung P1000 only to discover that it won't play over half the Blu-ray discs I have. (A little "hour glass" symbol appears on screen for minutes on end after which the player won't respond to any further commands and has to be physically unplugged to even eject the disc.)

Anyway, here are the discs it wouldn't play today:
Curse of the Golden Flower
Immortal Beloved
Spider-Man 3
Fifth Element (Remastered)
300
Fantastic Four Rise of Silver Surder
Old Boy
Pirates of Carribean: Dead Men's Chest

I've already requested a firmware update disc and will hopefully receive it before too long. Should this take care of the problem?

that should fix the issues with most of those discs.

How long did you wait, watching the hour glass, before giving up?
I've heard that a few titles take a good 2 to 3 minutes to load...

If you have a DVD burner in you computer, you can download the latest firmware disc image (.iso). burn it to a DVD-R and load it onto your player now.

fitprod

Don't have a burner in my computer, but I called Samsung yesterday and the rep said they'll send out the firmware disc right away. However, I've since heard that they sometimes don't send out the latest update, so now I'm worried.
For that matter, how would I even know if it's the latest one or not (outside of some of my Blu-ray discs still not playing)?

Since you just see an hourglass when it's loading, it appears that you have the oldest version of the firmware. Later firmware versions replaced the hourglass with something a little 'nicer'. So, even though you may not end up getting the most recent version available, you should at least get something newer, which will resolve most, if not all, of your problems.