I have deployed 3 RPis as digital signage systems. They work flawlessly for over a year now. I use another one as a home server for DNSmasq/VPN/etc. No issue and has more than 30 days uptime.
I share your views on SDCards but I don't consider the RPi 'unstable' by any means, although the SD cards get easily corrupted.
I had a 'bifferboard' (extremely small board) and an eBox2230. I know what unstable looks like, and the RPi is the most stable mini-PC at that I've seen so far.
I've got about 15 out for 8 months running OpenELEC. No problems so far.
I've also already ruined one (admittedly, cheaper no name brand) SD card on another raspberry pi. That one went after 2 weeks of hard usage. I now have an ever growing collection of SD cards (4 gig cards are too small for more than basic uses of the raspberry, even 8 gigs can be a bit limiting)
That said, the raspi's are fun, but I wouldn't trust the SD cards on them with something like this.
I never had the SD card corruption issues before, but I moved to this option just in case. I don't see the instability issues you talk about either but we're probably giving the Pi different uses...
[1]- http://www.raspberrypi.org/forums/viewtopic.php?f=29&t=44177
Used to have a lot of trouble with my RPi getting corrupted (fixed with a new power supply). And rather than spend any time trying to make everything read-only in software I figured I'd just use the "lock" switch on the sd card. That was when I discovered that the lock didn't actually do anything.