Chrome is telling you there is a problem because there, well, IS a problem. A problem with Flickr.

Check for yourself.. goto http://www.whynopadlock.com and put in the url: https://secure.flickr.com/

You'll notice that 12 of 37 items are insecure.

I have developed many web solutions that use both HTTP and HTTPS (example, you switch to HTTPS when logged in), neither of which are subject to this issue. The reason? I detect if you are in fact using HTTPS and adjust my content to use it as well. It's really not hard. Basically, Yahoo! needs to add an if statement somewhere that changes a variable from http:// to https://

Example (from Google Analytics):

var _gaq = _gaq || [];
_gaq.push(['_setAccount', 'UA-XXXXXXXX-1']);
_gaq.push(['_trackPageview']);
(function() {
  var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
  ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
  var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
})();

Look closely at this bolded part:

ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';

They check to see if it's an HTTPS request, and then set their base to the appropriate protocol, and in this case also a sub-domain.

Security standards are getting more and more demanding so it doesn't surprise me that Chrome would be the first to start being more strict about them.

There is also another problem with turning off the secure checks: while you are technically "fixing" the annoyance, you are now also opening the door to other websites to be able to bypass the restriction. I'm sure a lot of you view random sites, look at porn, and visit torrent sites.. all of which have been incubators for viruses and malware.