I suggest the same thing as well. Showing the flag of the country where the user resides in logs or anywhere on geocaching.com would be very interesting. I live in Canada and was surprise to read a log from a geocacher from Poland who visited one of my caches. If he would have not mentionned the fact that he was from another country I would have never known. I tought it was quite special that someone from another country was at my cache! Same applies when I go to the USA. I always mention in my logs that I made a very long trip from Canada to a cache that I found so that the owner knows that I am not just someone from the neighbourhood which in my mind makes it more special since I live far away and took time to stop and find that cache. Just adding a button in everyone's profile asking to show country flag yes/no and there will not be a privacy issue. It would be a very nice feature I think!
