Hi Robert.
Once you determine which version of a URL you would like to represent your site, the best method to enforce that decision is to use a 301 redirect. For example, direct all non-www traffic to the www version of the URL the same way SEOmoz URLs appear. With this approach, 100% of your URLs will appears as the "www" version in SERPs and there will never be any confusion or conflict.
I've heard people talk about using canonicals or setting the preferred domain in WMT. Neither step is necessary as long as the 301 is in place. The reason I still do both is I like to account for failures in a process. You never know when someone will make an error and modify an .htaccess file incorrectly and wipe out your redirect.
If you have the redirect in place, OSE and similar tools should clearly see the redirect and act appropriately every time. If the tool does not work correctly, I would examine the header tag of the page to ensure the 301 is working properly. If it is, then I would perform the same action you did and report the bug.
If you do not take the proper steps to enforce a "www" or "non-www" structure, you will see the results which you described. Some users will visit and link to each version of the page which will lead to both versions of URLs being indexed. Google will index a version based on which was discovered first or which version it deems more important based on links and other factors. When you perform searches for a site, some URLs will appear with the "www" and some without it. The backlinks will be divided and, as you know, that is bad for SEO. The duplicate content issue will set off alarms for the SEOmoz crawler and similar tools, but Google will still index one version of the page.
I am not sure if this completely answers your question Robert. If I missed anything, feel free to ask.