There's a lot going on with this one!
Ultimately, it comes down to this: The logo is an SVG loaded via an "external" sprites file using the svg markup
use xlink:href=.... (where "external" here just means the SVG code is not the same markup file).
This was being output like this:
<svg role="img" class="so-icon so-icon-logo" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-label="Stack Overflow Logo">
<use xlink:href="https://zgab33vy595fw5zq-zippykid.netdna-ssl.com/wp-content/themes/stackoverflow/assets/svg/output/symbol-defs.svg#so-icon-logo" />
Note that the URL being used is a full URL including the hostname of our caching server. This works fine for things like CSS files and images, but SVG support for pulling external markup from a different host is problematic at best.
What's interesting (to me) is that different people saw different errors and/or still saw the graphic. There were CORS errors, errors saying "Domains, protocols and ports must match", etc. On my machine, I got the errors in my console, but the graphic still loaded.
Anyway, ultimately, the fix was to just make that URL relative instead, which is now live:
Thanks for reporting this!