Despite nominal support from most modern word processors, and some limited support from professional typesetting software (with the exception of some software actually made in East Asia), you will run into serious unsolvable problems sooner or later. I have encountered problems with all of the following (in no particular order):
The usual “solution” to any of these problems is to give up (to typeset the text in some other way). A notable exception is right-to-left support: As recent as a few years ago, some people will go to the trouble of typing, say, a horizontal headline in reverse so that they will come up correctly when read right-to-left.
Culturally speaking, this lack of support is a very serious problem. As people work around the problems by giving up, the correct way to typeset things get less and less used, until they get forgotten by the native speakers (cf. the now-virtually-extinct CJK myriads separator vs the Western thousands separator). In other words, the lack of proper native language typographic support forces Western typographic conventions onto non-Western typography. In a sense, this is arguably a form of cultural imperialism.