The mixed content is, fundamentally, not secured by HTTPS. If your page is important enough to warrant HTTPS in the first place, why are you allowing user-specified content into the mix anyhow? Users are not trustworthy, in general.

Bear in mind if you implement the proxy solution that others suggest, you aren't just serving the content, you're approving it. Blind proxying is not really sensible; again, if it were, then why are you HTTPS in the first place?

You're probably talking about images. You should probably let them upload images and host them yourself, at which point you should actually examine them somehow for security guarantees, such as "yes, this really is a JPG".

If this sounds a bit utopian or a bit hardnosed, what it really comes down to is, do you need HTTPS or not? I won't necessarily guarantee there's never an in-between answer but it's an awfully narrow space. And if the answer is "yes", well, follow through then.

I believe hotmail handles this by proxying all external resources through their own HTTPS proxies.

Good question. If you mean specifically getting around the "some objects on this page are insecure" popups, a trick I've seen work is to cut off the http protocol portion of remote URLs, forcing them to look like "//www.example.com/to/file.jpg".