I helped tutor a Japanese couple (grad students) when I was an undergrad. They both spoke very passable english, but wanted to improve, and I was happy to cover the many cultural, pronunciation, and listening challenges that Japanese face. When I started to discuss the difference between Urban and Rural America... they at first refused to believe that Rural was a word. I learned some Japanese history/culture (one of the only times I've ever been invited into a Japanese couple's home!), how to pronounce a few phrases, and tried Japanese food (natto and nankotsu) that I wouldn't have otherwise.
However, after about 6 months the wife (who had studied English literature) asked me for help with a test she was (re)taking on English grammar. It was multiple choice English and about half the problems she asked for help on were impossible for me. Often, all of the choices seemed wrong, but I knew at least one must be right!
In the end I apologized humbly, and said that there were many things that were correct by the rules, but native speakers would find them so strange that they would likely be misunderstood. Also, something which apparently was not being taught (and needed to be) was ordering of adjectives in a description (e.g. fat bald white guy), which I made up on the fly (increasing order of permanence). Changing the order implies emphasis... but I had never noticed it as part of the language before, and neither had they.