To me the most annoying thing about non-native Polish speakers is that they exist, so I can never be sure I can talk privately in the presence of foreigners :)
When I was a student of English philology, one of my profersors was a Brit by the name Angus Macqueen (
URL) (Hi Angus). He was out Shakespeare teacher and a very nice fella. He spoke practically no Polish After a year or so in Poland he went back to Oxford for some time and then came back to Wroclaw University.
During on of the classes he suddenyl left the classrom and came back with a handful of chalk. One of the sudents made a comment (in Polish, to conceal the meaning): "what a fool, he could have asked one of us to bring the chalk". At that, Angus stopped jotting notes on the board, turned around and said with a funny Polish accent, but nevertheless correctly: "Nie jestem glupcem. Jestem poprostu uprzejmy" (I am not a fool, I am simply polite).
His Polish was eventually so good that in late 1980's he was a consultant and the translator for the documentary "Struggles for Poland" (
URL)