Sometimes I can best remember a question by its comments. How can I search for a question that way?
Downloading the data dump is not viable because it may be a question posted today.
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Since the top five comments of each post are displayed in the page, Google indexing can pick them up. So if you can remember key words from the comments, a Google search (with site:stackoverflow.com, of course) should be able to find them.
For example, I know I once made a comment with the phrase "four-year-old". I can use this search to find it again (the second link shows my name in the preview, so it's a pretty good bet).
You can't at the moment. It's annoying to me, too.
It won't help with other people's comments, but for your own comments to questions posted today, click your name at the top of the page to get to your profile page and then click on the "recent" tab near the middle of the page. This should show comments for the last couple days or so.
Additionally, to search older comments you don't have to download the entire data dump. Just use http://data.stackexchange.com
You can use in your profile
activity tab with