Basically, if you are an obvious foreigner, most women will assume that you call them Fräulein because you are using the conventions of your own country and not take offense. This might change if you insist on it after correction.

The same thing applies to many other faux-pas in social etiquette as long as they are honest mistakes. It is not the same thing as calling someone the German version of a**hole since I won't believe you that this is polite in the US.

It is a bit hard to answer your question because it is actually an English question as well: What polite English phrases are impolite/unused/misunderstood in German?

Something that you should look out for is that Americans can actually be "too friendly" for German speakers, as in superficially friendly and not meaning it. Your "polite" may be someone else's "hypocritical" and someone else's "honesty" can be "rudeness" for you. (But take this with a grain of salt because my knowledge of US norms is spotty.)

E.g. I will certainly not tell you that you are welcome to visit me if you come to my city if I don't mean it.

This is a great problem because people will perceive it as your character (and vice versa) and so they will not explain it to you.

I remember that language schools like Berlitz actually have courses on cultural interaction (so that US people can negotiate with Chinese, say).