I have a one-day-old 12.10 install on a Dell machine with an ATI Radeon 6450 graphics card, and two Samsung monitors (one connected through VGA, one DVI). I also have disk encryption enabled, and I'm using classic GNOME instead of Unity.
This all started with a different problem, actually: when I rebooted the system, the BIOS would load, the purple background of what I assume was GRUB appeared for a few seconds, and then both screens would go into power save.
At first, I got around this by simply hard-rebooting when it got "stuck," and everything was fine. Today, I tried hitting some random keys, and surprisingly, the disk encryption screen came up. When I logged in, however, one of my monitors (the DVI) worked fine, but the other (the VGA) looked like this. (By the way, I'm using TwinView or whatever the equivalent is; that is, I'm not mirroring monitors.)
The picture isn't good, but basically it's a solid color similar to whatever color the desktop background is, with lots of slightly darker vertical lines. Changing the desktop background changes this solid color. If I change to "mirror screens," this monitor displays a solid gray color.
Initially, after one reboot, I also had to deal with a different problem where I couldn't log in through X (due to ~/.Xauthority changing owners). While I was trying to fix that, I rebooted a couple times and messed a bit with my ~/.config/ (deleted monitors.xml) and /etc/X11/Xorg.conf (tried to generate a new one), and had some even weirder things happen, e.g. mirrored screens where one was translated about a quarter-screen to the left, and then wrapped.
But now that part's fixed, and I'm still left with one working monitor and one solid-color monitor.
To be honest, it might be easiest to just do a fresh install, but I'm worried the same thing might just happen again (maybe it's a hardware thing?)
EDIT: some more info--if I change to lower resolutions, that monitor starts flashing madly...