I spoke to the support guys at Woo and they are telling me this is a JetPack issue.
Please see http://proof.janegoodchild.com as you can see, in the source code, the WooCommerce scripts are placed twice (in the head, and in the foot). This only happens when JetPack is activated and signed in. If I sign out of JetPack or deactivate the plugin, it fixes it.
We'd like to keep using both, so can you tell me what the problem is please?