Here's how to fix this problem.
Open Mozilla Firefox's
about:configaddress. Search for
font.na. Find your languages character set (it's usually in the html meta tags, type ctrl-u to view the source html, then press ctrl-f to search).
For Japanese text the charset will be
font.name-list.sans-serif.ja. The default is "MS PGothic, ＭＳ Ｐゴシック, MS Gothic, MS PMincho, MS Mincho". Simply add your unicode fonts to the beginning of the list, separated by commas, in the order that you want your operating system to use them. In Windows you can add Arial Unicode MS, so your list will look like this: "Arial Unicode MS, MS PGothic, ＭＳ Ｐゴシック, MS Gothic, MS PMincho, MS Mincho". The Code2000 typeface supposedly supports the most characters, but is ugly as hell. Lucida Sans Unicode or Bitstream Cyberbit is probably much better. There's a great list of unicode fonts in wikipedia.
What looks better? The first text, or the second one? (note: these fonts are scaled up in size)