Hmm, I've used the gaijin card a few times, though it doesn't work as well for me because I look Japanese, and I'm a Japanese citizen. Though on one occasion, I made the situation worse by unintentionally using the gaijin card.
I had a teiki to go from Shioya to Suma, which are one station apart, but on that day I was hurry and I had to go to Sannomiya, which was six stations away (theres only one JR line in Kobe), and so I forcefully went through the tickets gates without adjusting my fare and adding the appropriate 170 yen. Unbeknowest to me, a plainclothes officer had witnessed my barging through the gates and followed me out of the station. He grabbed my arm, stated that he was the police, and immediately demanded that I hand him his wallet so that he could check my ID. Now because he was in normal clothes, I was pretty sure that this strange man who was demanding to see my wallet was trying to trick me into stealing my money or something. In my broken Japanese (I really did speak broken japanese then, because I had spoken English most of my life), I said something like "Badge oh misete kudasai" - please show me your badge. Unfortunately for me, this was probably the last thing I should have asked him because his face reddened, he flashed me his police badge, and he dragged me to the nearest police box where he took me to the second floor in a little tatami floor and yelled at me for 30 minutes. I honestly did not understand what he was saying but he did speak great agressive kansai-ben.
Now I know I broke the law and cheated the station, but I don't know why the cop got so mad. Was it because I looked Japanese but he thought I was trying to use the gainjin card? Is there some rule that you should never ask to see a cop's badge? Though I do wish he had beaten me on the head with a phonebook because it would make this story a lot more interesting, but alas, I only received 30 minutes of intense yelling.
Of course, 99% of my other encounters with the law were much more pleasant and the cops are usually very polite, as long as you cooperate.