As an American living in Japan, I know how surprised Japanese can get when foreigners internalize the society around them too much. At J-List, the Japanese staff have gotten used to me doing things like bowing while speaking Japanese on the phone to someone or pulling out a kotowaza (Japanese proverb) to make a point. According to an interesting online poll, some other things gaijin do that surprise Japanese include speaking using dialects like Osaka-ben, singing enka songs at karaoke, giving dates in the Japanese calendar system (e.g. Showa 43 instead of 1968), drinking fruit-flavored milk with a hand on one hip after a bath (it sounds odd, but I do it most every week), and sitting seiza, or in proper Japanese kneeling position. Another thing that surprises Japanese people is when foreigners are polite, or when they line up properly in crowds -- it seems sad to me that this kind of behavior be the exception and not the rule. When Japanese go drinking with a foreigner, they always seem to expect him to order a Budweiser, since that's what all foreigners drink, right? But I'm much more likely to ask for atsukan, or hot sake, which always seems to surprise Japanese around me. The holy grail of a foreigner living in Japan is when a Japanese person temporarily forgets how to write a difficult kanji and you casually jot it down for them. That's only happened a few times to me, but it was glorious, let me tell you.
Arumikan ni aru mikan is another thing the Japanese don't expect you to say.