I drunkenly told a professor something fundamentally wrong about a friend's thesis work. Should I clarify and/or apologize?
I don't see why Germany should be any different from other places, but generally it is a good idea to apologize for stupid things said drunkenly. And since this may have a bearing on the reputation of a third party you probably have an obligation to make sure the record is correct. 

Sooner is better than later in such things, so the professor doesn't spend effort on a lost cause.