Mixed scripting happens when an application served via https references resources including CSS,XML,JS from domains that are not served via https so a typical example would look like this:
|googleusercontent mixed scripting vulnerability|
So why is this a problem? well because it means in a Man in the middle attack you can influence the behaviour of a trusted domain without mirroring the entire domain! You can have your victim---during a mitm attack---use the services on their trusted domain with out having to use sslstrip or other anit-ssl tech you don't need to touch anything on the ssl layer because the application inherently serves unauthenticated content to the user! All you really need to accomplish is mapping the unauthenticated domain to a machine under your control.
So then how does this tie into the Google Web Cache? It turns out google webcache also suffers from mixed scripting!