So sorry for the time it's taken to get back to you on this - I had to test some things out.
There definitely shouldn't be broken image links as are being displayed. There are a couple of things we can do to resolve this. It's most likely because at the time WordPress.com took a snapshot of your site, that the WordPress.org self-hosted sites couldn't be reached - for whatever reason. This isn't anything to worry about, but explains why you are getting the result you are.
To fix it, you should disconnect each blog from your WordPress.com account, reconnect it, and then test it with a fresh browser cache.
To disconnect, go to your WordPress.org site's dashboard, browse to the Jetpack plugin menu, and in the top right, hover over the 'Connected to WordPress.com button' - it will change to red, and prompt you to disconnect.
Here's a screenshot to explain further:
Once you're done, reconnect, and clear your cache to ensure your browser is downloading the most recent version of the site. There are instructions here:
Then check out your WordPress.com blog list again. Let me know if this works... which it hopefully will!