I have a jsf application that works fine in Internet Explorer over http. But when I run the same application over https, I get many jsf errors, such as object does not support property or method, or 'xxx' is undefined.
I'm not sure where to even start to determine the nature of this behavior. Any ideas where I can start or what might be causing this issue?
Well it has nothing to do with HTTPS, using a different transport protocol is not going to magically make classes on the server lose their methods and properties.
Start with the server logs, there must be a clue in there. If not you'll have to figure out how to make your particular server software provide more information.