Were you using Cloudflare or Cloudfront? You mentioned both.
I am sure if you don’t use the minification settings on Cloudflare and especially not Rocketloader and high security settings, that you won’t have issues. The only thing that concerns me is that Cloudflare does not clear cache when a site is updated. Also, as mentioned somewhere, it is important that we don’t cache everything with page rules.
I am interested to know if the developers of Comet Cache have an opinion on this and what their advice would be regarding the best settings on Cloudflare (not Cloudfront) and if there is a way that Comet Cache can control Cloudflare behavior, so it does not interfere with the great job Comet Cache is already doing.