Analytics and filtering?
Just checking.
Using SSL will stop any intermediate network hops to your target snooping on your content (such as your ISP for security or profit).
However Google as the end point of your search request will legitimately decrypt your search request before executing it.
As far as I know Google routinely passes back a URL which contains not only the target web site but also a string of search terms used (presumably to show the target that they were found via Google and aren't they lucky).
If the URL returned is to a dodgy site with loads of pron which also supports SSL this is surely where the problem starts if you want to monitor content to protect the kiddies.
Google can presumably implement a Safe Search policy at their end, but this would require you to log onto Google before you could search? Ah, it is an option in Google which doesn't requie you to log in so presumably a cookie.
So - why does encrypting your search request prevent Safesearch from working?
Are they filtering the search request on the fly before it hits the search engine and so working on the encrypted data stream?
Sounds like a quick fix solution without any proper system design if it needs encryption turned off at source for it to work.
Likewise harvesting search terms - if the eventual target of the search gets the key words tacked onto the URL then the only people to gain from the search being in clear are intermediate snoop points.
Supplementary - if Internet Cafes have to suborn SSL sessions to filter for bad stuff then presumably you should always use a VPN when surfing away from home.
Supplementary 2 - presumably the padlock doesn't show if your HTTPS session has been redirected?