... Vista's the 'new thing' though, right? At the moment it's not necessary, but won't we start seeing vista-only games released once it's been out for a few years and covers the bulk of the windows market?
Yep. I wouldn't upgrade to Vista now, and won't for some years I think, but if I bought a new computer now I would get one with Vista on it (and then I'd put ubuntu on dual-boot).
Anyway, poor old LuckyRaccoon, you've obviously already got a computer with Vista and don't want to hear all this. It sounds like Lazy_Perfectionist's idea with the compatibility mode might help. The first thing though is definitely to upgrade your video drivers.
And run windows update. There aren't any that deal specifically with Dominions, but there have been updates that improve compatibility with a long list of programs, some of which are games. Don't need to install them all, just look them over, see if any might help, then decide which ones are worth installing. DirectX, I recommend you update that if there are any new versions available.