I think that a lot of interwar German artistic and cultural movements (German Expressionism in particular) were influenced by or were a reaction to the precarious financial and political state of the fledgling republic. A stable democratic state that successfully overcomes the global depression of the early '30s would definitely shift the focus of the German Expressionist movement away from themes of alienation and disillusionment.
Also, without the Nazi rise to power, a number of dissident film makers and artists (I'm thinking Fritz Lang in particular), wouldn't have fled the country. I definitely think Lang's ATL film career might be worth further discussion.
If the Nazis never rose to power, what would German culture look like in the 50s?