Try as I might to be a careful webmaster, mistakes creep in.
I'm not sure why, but I ended up taking a peek at Google's webmaster tools and noticed I still have about four or five 404s. Why? Well, two of them were mistakes I made: one, I tried to link to Wolfram Alpha and forgot the "https://"" in front of the URL. Another, I simply forgot to put ".html" on the end. I'd like to eventually remove that requirement and remove the .html from every canonical URL, but doing so would involve some AWS/S3 ninjutsu that I presently can't be bothered to work out.
While checking these things out, I noticed that my 404 page over HTTPS was disgusting. None of the stylesheets are loading, because they're linked to over cleartext HTTP - but that shouldn't happen. It took a few minutes to figure out, but CloudFront was pointed to an old URL for the 404 page, which still exists but isn't updated. So I fixed that, and blew away the old files, and hopefully there's no more issues there.
The last two 404s I can't figure out - the month is wrong on them, but nothing I've ever written links to the incorrect page, yet Google insists that the sitemap and ATOM feed both link to it. Requesting a live copy of both those files suggests otherwise. No idea what's going on there.