I recently updated to WordPress HTTPS. I use it with WooCommerce 1.6.1. When I force HTTPS exclusively on the checkout page, the checkout page is blank. I un-check the force on the check page and it returns. However, even just having WordPress HTTPS installed (but not actually forcing anything) makes the WooCommerce USPS shipping module go into an endless search mode whereby you can never checkout. When I disable WordPress HTTPS, all of these problems resolve completely.
I am not sure how to make this a public test because I can't put this configuration on my production site. I'll see how else I can set up a test site. But I thought I'd submit this to make the developer aware of this issue.