Marshall, this is kismet - I'm coming here to explore this very same issue, with a few more details, and a twist.
Visualize two pages, and given that the secure page often uses the same resources over https as http - a header image, for example. Let's call the may-or-may-not-be-all-secure page /about, and the secure page /purchase.
Browse to https.... /purchase, everything is fine, green light on secure items. Use a link or even make a direct request back to /about, and you get a mixed content error. On this page is a link back to /purchase, but you don't even have to do that - change the URL to /purchase in the address bar.
The previously secure page now displays insecure items (and Chrome doesn't make it easy to tell you what they are). WTH?
Basically it caches the insecure items from the previous page state, but only in the context of that tab (as I understand it, anyway . . . )
I've done some searching and this is due to caching, there are many proposed fixes (clear history, open a new tab, whatever) but the really BIG problem with this is the average user won't have a clue how to do any of this or know what it means. Insecure = bad, close and shop elsewhere.
Has anyone solved this to any reliable degree? With Chrome gaining market share, it's become the "new I.E." in terms of the thorn in a developers bum . . . .