I don’t see any discussion of an “advanced” search mode, but I’m assuming it’s somewhere on the horizon. One suggestion I have about search in general is that it would be really cool to have a way to get RSS and/or bookmarks for a specific search, a la craigslist. This would enable users to build their own custom view of a forum, making it almost seem like custom-tailored subforums.
Also, having implemented a backend search index before, I know that certain types of information are pretty easy to stick in the index (assuming you’re using something like solr or elasticsearch) and that the simple task of just coming up with a list of what attributes you want to index can be an ongoing effort, so perhaps it would be helpful to have a list of user suggestions for searchable attributes. For example, it would be cool if one of my search terms could be replyto:hamburglar. Or numposts:100+. Or
category:foo OR category:bar". Thinking up novel attributes to search on is one way Discourse could distinguish itself from the forum status quo.