When I lived in Germany, I found it useful to mumble. The listener would usually give you the benefit of the doubt, and often figure out what you meant to say.
On the other hand, to speak clearly and distinctly will prove you DON'T know any grammar, and they can be a little critical.
The worst mistake I made was to rehearse what I wanted to say in my mind, so that I could spit it out without stumbling. Trouble is, if you do that your listener often assumes you know much more German than you really do. The answer would come back like a machine gun, and I wouldn't catch any of it.