Better than "Peking". I always wondered if the "old" western versions of Chinese place-names came from some other dialect than Cantonese, or just a general careless mangling by the British. Probably some of both...
There are few avenues for misunderstanding that Chinese people and "Westerners" have left unexplored. Just to scratch the surface, there are:
Romanization problems. Imperfect and changing systems for writing down Chinese in the Roman alphabet. This is how Chou En-lai changed to Zhou Enlai, and Mao Tse-Tung became Mao Zedong. The habitual omission of tone-marks from English-language texts makes correct pronunciation, and therefore
meaning, a matter of guesswork. Untutored readers will inevitably pronounce the letters of the romanization in the manner habitual in their own language, producing ear-bleeding solecisms like pronouncing Cáo Cāo (one of the central characters of
The Romance Of The Three Kingdoms, and many anime, comics, video-games etc.) as "Cow Cow" (it is "Tsao Tsao"). For English-speakers, correct reading of the old Wade-Giles romanization, or modern Pinyin, requires study. Only the Yale romanization (developed for the US Army) was created with the specific intent of making it relatively easy for native English-speakers to approximate correct Chinese pronunciation, and in many ways it's a pity it went out of style.
Geographic confusion problems. Applying the wrong name to places because the European asking "What is this place?" and the Chinese person answering didn't really understand each other. For example the city now known as Guangzhou (pron: Guang-jo) was called Canton based on the local pronunciation of the name of the
province, Guangdong, in which the city is located.
Indirect adoption problems. Some English names for Chinese things are adopted from languages other than Chinese ones. One example is the word "China" itself, which comes from Sanskrit via Persian and Italian. Another is "Mandarin", a Sanskrit word adopted via Malay and Portuguese, meaning something like "counsellor" or "minister". Mandarin Chinese is so called in English, because it was the language spoken by officials, as opposed to the many other regional languages.
"Dialect" problems. The "official" language of China has been based on the North Chinese "Mandarin" family of languages for hundreds of years, but Europeans often entered China from Southern coastal regions where other languages like Cantonese, Hakka, Hokkien etc. were, and still are, spoken. Even where the words are the same, and quite often they are not, the pronunciation can be very different.
Language change problems. Like any other languages, Chinese ones have changed over time. The first European scholars to study Chinese language seriously were Jesuit missionaries in the 16th century, and they created the first Romanization systems. We still use many of the names they invented, such as Confucius (Kǒng Fūzǐ), but in some cases Chinese has changed since their time, leaving their romanizations behind like fossils.
The case of Peking is a combination of the last two. The word Peking originated with French Jesuit missionaries and is based on an old pronunciation that altered in a subsequent sound change in Mandarin. The pronunciation "Peking" is also close to that used by speakers of the
Fujian "dialect" around the port city of Xiamen, through which much of China's early contact with European traders, missionaries took place. "Beijing" is closer to the Northern Chinese pronunciation, and is now of course the officially correct one. Bear in mind however that "B" is less "explosive" in Mandarin than English, and can sound quite close to "P" to the untutored ear.