More than the phrases themselves, I think that it is important that Anglo-Americans and Germans understand each other's "different mind sets." Using the guidelines below (and similar ones) will prevent many misunderstandings.
The first thing is that any statement made by a German is "heavier," more serious and more definite than a similar statement made by an American (a Britisher is probably an intermediate case).
For instance, if an American says, "he is a good friend of mine," it means this is someone I know "pretty well" (ganz gut). If a German makes this same statement, he's saying "This is one of my top five (or so) best friends, (someone I could count on to take care of my children if anything happens to me)."
If an American says, "what don't you drop by on me the next time you're in town," it's not "insincere," but it means "why don't we try to get together?" (But there's no tragedy if we don't.) If a German says that, he means, "I definitely want us to get together because I have something I want to show you (a new house, spouse, or child, etc.) Meaning that it would be said only to a "good friend."