Is there a way to get past versions of an app in App Store? Say you're running Snow Leopard, and there has been a 10.6-compatible version of an app, but the newest version requires Lion or greater. Or, say an app recently received a UI overhaul, and you'd like to buy the version that came before it was changed (perhaps the folder structure changed and broke your applescripts, or you just liked the old one better).

App Store only shows the most recent version of the app, so is there a way to get it to show an older version? I know, you can sometimes try buying directly from the developer, but that's not always an option, and it'll become even more rare as time goes by.
It's not an option as far as I know. If it's an app that you purchased previously, you should be able to roll back using Time Machine (you're using Time Machine, right?). You might also have to roll back the settings files in your Library folder if you want your old settings back.

But if you are looking to purchase a new app you are stuck with the most recently available one.

The good news is that apart from Apple's own software, most developers choose to offer their software directly as well.