Two people updated their site's favicon and the directory kept showing the old one. Zach Ware's card showed a purple square when his site has an American flag, and K. Elizabeth Coggins's showed a generic gray cube instead of her photo.
Turns out I was getting every icon from Google's favicon service, and Google's copy can go stale for months. DuckDuckGo has an icon service too, and it fetches your site's actual current favicon. So now I ask DuckDuckGo first and only fall back to Google when DuckDuckGo comes up empty. I tested it by hammering their service with all 87 sites at once from my server, four times in a row, and it never once complained.
Nerdy detail: DuckDuckGo hands back your original favicon file, which is what makes it fresh, but originals can be huge. One site's icon is a 108KB PNG. Anything over 30KB still gets Google's tiny resized version instead, so the homepage stays fast.