Namely concerning phishing. There are a lot of characters that look the same or very similar in diverse typescripts — for example the latin A and the cyrilic A look identical. Just as the latin B and the cyrilic B (which means ‘V’). This way you can have several domains registered that *look* the same, although they differe in one character (or more) that just looks identical. Just imagine dozens of http://paypal.com or http//amazon.com phishing pages because of that.

It has been debated in the past already whether it should be possible that the URL’s could be written in Unicode and was decided against it for that reason.