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I would double check and make sure that all your campaigns: Email, Bing/other networks PPC & Retargeting ads etc. All have Google's utm parameters setup on them.  These are all areas that webmasters tend to overlook.  The PPC ads tend to still be listed under organic search, but you can't segment out the paid or non-paid Bing (other network PPC) traffic without the tracking installed.  Here is a great blog post that Avinash wrote on tracking direct traffic correctly.  I would start here and make sure you have everything setup correctly before looking for other nuances.  http://www.kaushik.net/avinash/2010/09/excellent-web-analytics-tip-analyze-direct-traffic.html

It sounds like the scenario you're describing isn't an issue of the URLs changing, but more so content shuffling within given URLs.  This is VERY common.  Google even promotes this with the Website Optimizer as they understand that a users experience with a website can vary from user to user, and having the flexibility to change to meet a specific user's needs is a good thing not bad. Unless the shuffling is dramatically affecting your own search traffic goals, I wouldn't be too concerned with it. Mostly I'd recommend strong categories for your pages that target your key search demographics and the archival of pages that have come and gone in their voting cycle.  That way you'll have plenty of static content to work with as well.