My community is online, but many of the images and JS are failing to load.  The browser console shows images having an error:

kCFErrorDomainCFNetwork error 303

Some basic googling indicates this is some sort of caching issue. I use memcache and I also use Cloudflare.  But when I clear the IPS cache (using the Support link, which automatically clears things), and when I put CF into "development mode" (where it bypasses the cache)... the behavior doesn't change. 

Anybody familiar with how to troubleshoot / approach this?

Are you experiencing problems with all browsers or only specific browsers?

That error seems to be Apple-specific.