Let's see what the non-UK responses are like...
So, what's your pick, shanks? Having had contact with people from many different parts of South Asia(Gujarati, Bangladeshi, Burgher, Punjabi, Telugu) since childhood, I have happily never been guilty of the gaffes you mention. The hardest thing I find is trying to explain where my Dad is from. Although he was born in Meerut, but his family home was only ever Quetta or Karachi, while he attended boarding school in Ghora Ghali. So I find myself saying something really long-winded like "he was born in India, and grew up in what is now Pakistan." Any suggestion on a suitably catholic term for those from the subcontinent, from one of "your people" (is it wrong that I cringed and smirked simultaneously when I read that phrase?) would be much appreciated.
For my father the irony of this identity dilemma is that he was stateless for forty years - Britain would not recognise him as a citizen nor would India, so that when he became a naturalised NZer, he had lived here longer than had the NZ-born immigration officials working on his case.
As an aside, Enigma suggested that my Dad was not "stateless" for forty years, but "stately"! It also occurred to me that its inevitable suggested replacement for NZer, O'Brien, may have deeper meaning. Terence O'Brien served as NZ's ambassador to the UN for years, including the duration of NZ's stint on the Security Council. That quirky coincidence seems apt for our beloved spell-checker.
