It means that you cannot conveniently have both Japanese and Chinese text in the same document, even though you're dealing with an encoding that is supposed to solve internationalization problems.

The "multiple code points" problem also creates complexity, and that complexity can lead to security holes. See [link|http://www.schneier.com/crypto-gram-0007.html#9|http://www.schneier....-gram-0007.html#9] for the kinds of security problems that could happen and [link|http://www.schneier.com/blog/archives/2005/02/unicode_url_hac_1.html|http://www.schneier....de_url_hac_1.html] for a concrete example of it being exploited in practice.

Cheers,
Ben