1) They don’t understand the subtle usage of British swear words, so it’ll end with confusion. They aren’t generally able to deduce the intention of the word from its context and sound, and will often ask what it means and why you said it. Which is quite hard to explain really.
2) The use of the F word is different. It’s used to make a point or else very ostentatiously to show off what a macho hard guy you are. This may present a different image to the one you intend. However whenever I’ve used the F word in an understated British style they’ve realised that it’s a different usage.
3) Don’t use the C word. They don’t have the concept of swearing at your friends quite so openly, so stay away really. I’m not sure I’ve heard an American say it, and certainly not in normal conversation.
Stuff that doesn’t get starred out on this forum is probably ok, but they often don’t know the nuances of them either.