Is there a way to get past versions of an app in App Store?
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.