Unicode domain names
The stinger is that some scripts have characters visually indistinguishable from characters in other scripts.
Cyrillic ІЈАВЕЗКМНОРСТУҮХ are lookalikes of ASCII characters, but are NOT the same.
[If your browser isn't Unicode aware or you don't have a Cyrillic font installed, that won't make sense. Note also that these are drawn from the Unicode "Cyrillic" range, and not all of these are necessarily used in one langauge.]
Thus you can have a Cyrillic TLD *.СОМ that is wholly distinct from the existing *.COM. Can we say phishing on a grand scale? There, I knew you could do it! You can always depend on the El Reg readership!
I'm none too certain how to handle this kind of thing. Perhaps browsers will have to be told what script/language/Unicode block [*] to display, and convert everything else to some kind of canonical representation in ASCII digits? I sure wouldn't want to be the dude who's tearing his hair out over this!
* Footnote: scripts, languages, and Unicode blocks are not synonymous. You might think that any given language is written in one script, but no. Serbo-Croation is written in both Latin and Cyrillic characters; Abkhazian has Arabic, Cyrillic, and Georgian representations. It's enough to drive a man to drink.