For more information about the issue in general, and how to fix it, check out our blog post When Good HTML FanGates Go Bad, as well as the following great step-by-step guide: Switch to HTTPS Now, For Free.
UPDATE: Chrome 30 now no longer display "mixed security content" by default, as well as Firefox.
Are your HTML Fangate tabs currently showing as blank inside Facebook?
Firefox recently made an update to their browser that's causing these display issues. With the release of version 23.0, they no longer display "mixed security content" by default. http://www.mozilla.org/en-US/firefox/23.0/releasenotes
Facebook uses HTTPS by default now, so that means any content you host in our tab will have to use HTTPS as well to display properly. For images you can use http://imgur.com as a free hosting solution just by changing the links to HTTPS. If you're hosting other files from your own site, you may need to get an SSL certificate if you don't already have one and change the URL to HTTPS. These can often be found for under $20/year, and you could use one SSL certificate to cover many fangate tabs.
This has always affected non-secure content in tabs, but with more users updating to the latest version, this issue is becoming more common. If you would like to know how to fix this issue on your own computer you can go to http://mzl.la/13jCUSU.
Note: It's possible that some tabs will get a security warning from Woobox, even though there is no insecure content present. We are working on discovering why this happens, and hope to have a patch soon. This message only shows up for admins of the Facebook page, so end users are not affected in any way.