Whatever you think of cultural imperialism, English rules supreme and any city that wants to consider itself global will accommodate English speakers. However, this doesn’t mean the English is good, even in places that really should know better.
In Hong Kong the standard of English is predictably very good, since it was under British control for around 150 years, although there is the occasional double entendre that likely as not is probably deliberate. In Taipei the English used on road signs is somewhat abusive of the use of capitalisation, but most of the people & places I came across had a comparable mastering of the language.
Personally I think this is down to how China has progressed rapidly, and as a result there are things that are done based on expediency rather than strict correctness and/or elegance. In the case of English use, Chinese language use such as its subject-first structure (English typically puts verbs first), leak through.
For those who want to read on, there is engrish.com..