Edit wp-admin/index-extra.php.
Change this code (on line 10 or close to it):
$rss = @fetch_rss('http://feeds.technorati.com/cosmos/rss/?url='. trailingslashit(get_option('home')) .'&partner=wordpress');
to this:
$rss = @fetch_rss('http://feeds.technorati.com/search/'. trailingslashit(get_option('home')));
Personally, I changed my incoming links to use Google Blogsearch instead, as I think it gives better and more relevant results than Technorati. Just use this code:
...
$rss = @fetch_rss('http://blogsearch.google.com/blogsearch_feeds?hl=en&scoring=d&ie=utf-8&num=10&output=rss&partner=wordpress&q=link:'. trailingslashit(get_option('home')));
...
<h3><?php _e('Incoming Links'); ?> <cite><a href="http://blogsearch.google.com/blogsearch?hl=en&scoring=d&partner=wordpress&q=link:<?php echo trailingslashit(get_option('home')); ?>"><?php _e('More »'); ?></a></cite></h3>
...
Obviously you need to replace both lines... if you don't immediately see what to replace, you probably shouldn't do it.