On the forum, it looks like you cannot bold or italicize Japanese text unless it is at the beginning of a sentence or after a space or comma (maybe there are other cases).
Using the ** formatting:
例えば、この文。(whole sentence works)
例えば、この文。(beginning of sentence works)
例えば、この文。(after comma works)
例えば、この文。(middle of sentence doesn’t work)
例えば、この文。(middle of sentence doesn’t work)
Looks like using the <b> tag works
例えば、この文。
例えば、この文。
Yeah, using BBCode or HTML should work. Only markdown sometimes doesn’t work. Unfortunately using the buttons at the top of the text box inserts markdown.
That’s incredibly weird.
##例えば
こんにちは、皆さん！
Oy, mates! This ばか here is getting on my nerves! 俺のばか先生だな。。。
(weird tests)
This thread feels unresolved. Maybe something to bring up at the Markdown forum.
It’s works the same way in Japanese as it does English:
[non-word char]**[nonspace][anything but newline][nonspace]** == bold
where [non-word char] means whitespace, punctuation, or start-of-line.
I suppose that makes html better for formatting text, then.
… Unless if Discourse turns html into markdown. Good to know! 
This catergory pertains to bugs and errors for the app.
@rfindley pretty much nailed it. Markdown requires spaces around the bolded elements.