A comment on the "Call Us X" thread raised the Beijing/Peking question. As I understand it, Beijing is the more accurate pronunciation, and now that the shift has happened, it's probably for the good.
But there too I'd counsel against condemning people for sticking with the pronunciation that they've used all their lives, whether the condemnation is on identity politics grounds (you Western imperialists calling our places by your names) or on supposed error grounds (what a fool you are for mispronouncing this term). In many languages, foreign place names get translated. Partly this is to track the natural sounds of the language (which is why people mock those who abandon normal English diction when using a foreign, often Spanish-language, place name), but partly this is just an accident of history.
English speakers say "Moscow," not "Moskva"; would we say that "Moskva" is more correct, or just that "Moscow" is correct in English and "Moskva" in Russian. Russian speakers say "Reem" instead of "Roma," just as English speakers say "Rome." French speakers say "Londres" instead of "London." Russians pronounce "Warszawa" much like Poles do (despite having a different alphabet), while English speakers say "Warsaw." The Poles retaliate by calling Italy "Włochy." Deutschland can be Allemagne, Germany, or Nemechyna (transliteration from Ukrainian imprecise), and while the Italians, I'm told, call it Germania, they call Germans Tedeschi. That's history for you, both the history of one country being known by the names of different groups, and the history of phonetic and orthographic modifications in translation.
If everyone started calling places by their native names (setting aside cases of political controversy, and making allowances for the target language's sounds and cadences), that would probably be good; as I said, I'm glad that we've shifted to Pinyin from Wade-Giles. But let's keep some perspective, and recognize that this is a longstanding feature of many languages, one that's probably most aptly fought on grounds of practicality than ideology or even abstract "correctness."