Having been to Taipei several times myself, I'd say that it is no better or worse than any Asian city. but that's really just prejudice. I will concede, however, that Taiwan had the value of hygiene worked into them during the Japanese rule. In the first ten years of the 20th century, there was 49 newspaper reports of public urination leading to a formal warning by the police in Taihoku alone (ironically, more than half of these high-profile cases were perpetuated by Japanese), and public record shows that thousands of people of all sorts of background were fined every year for the same offense that did not make it to the news.[0] This really goes to show that the colonial government took the concept of hygiene very seriously, but even today some people will just do as they please.[1]
[0]: https://books.google.com/books?id=AKi5Wm5Mu_UC, page 27
[1]: http://news.cts.com.tw/cts/general/201001/201001030380454.ht...
I'd say it's more to do with development than anything else.