Attempting to link to a site that uses non-alphanumeric characters in its domain name is incorrectly encoded to Hexadecimal "safe" characters instead of punycode.
For instance, clicking on this links to encodes the link instead of linking to http://domaintest.xn--q9jyb4c/.
Also, attempting to write something with non-alphanumeric characters does not recognize anything past those characters as part of the URL.
The real problem here is not the lack of punycode encoding, but rather the inappropriate application of percent-encoding to the domain part of the URL. Simply leaving the Unicode characters in the domain name un-encoded, as in:
<a href="http://www.domaintest.みんな/">this</a>
makes the URL into a valid IRI, which all modern browsers support.
The fact that Chrome, apparently, also accepts the invalid percent-encoded domain names (and decodes and re-encodes them as punycode) does not make this behavior correct or desirable.
Addendum: Another related problem, which I did not realize earlier, is that the SE Markdown converter does not support un-encoded Unicode in URLs.
This should really be fixed properly, by adding true RFC 3987 IRI support to the converter, but in the mean time, a sensible work-around would be to at least make the "Insert Hyperlink" button in the Markdown editor use Punycode instead of broken percent-encoding for IDNs, as suggested above. This does require some non-trivial processing, but fortunately, there are existing libraries available for it.
Ps. Version 1.18 of the Stack Overflow Unofficial Patch user script now contains a client-side fix for this issue. The fix consists of two parts:
A monkey-patch to the Markdown editor "Insert Hyperlink" dialog that converts any URLs entered through it to use Punycode host names (using the punycode.js library by Mathias Bynens).
A content filter that automatically decodes any inappropriately percent-encoded host names in existing links within posts and comments.
