Er... unless you set up a redirect too... that "preferred domain" thingie won't do anything else than what it claims to do...
It will only DISPLAY all your results as www or non-www.
And give G a reason to check one version to the other.
They won't automatically drop the other version, i learned this the hard way... and since they don't, and since it displays the same content on two different URLs...
It may very well be that the homepage was the first to be spidered without the www, considered as a duplicate when compared to the www version, did not make it to the index, and thus NO links were followed from there. The rest of the pages are "displayed" as your preference but may not have been crawled on their preferred location ever since... did you check the cache dates?
But i'm just guessing.
So all in all it's probably the fact that you don't have a redirect from the www version to the other.
Put up a 301 redirect in the root directory to match your preference ( www to non-www ). Allow about ten days for the www homepage to drop out ( it'll become supplemental because of the redirect... if not the dupe content ;) ) and see if it makes a difference. You know, even WITH the redirect the old version will stay for some time ( as supplemental ).
You won't be able to check whether a page really is crawled at its new URL or not for all results will be displayed as your choice indicated.
You can try to look at the cache dates / the URLs in the cache. The -inurl:www doesn't seem to work all that well ;)
Also if there's a change that was made more or less at the time of the redirect, you can check the pages by looking for that expression. Likewise... an added navigation link, refreshed information, anything that is the same in the template, and IF not found it means that page is still the old version ( or the new... or whatever, i'm confuzed :) Oh wait... you're beofre adding the redirect. Add something short and useful, or modify something that's easy to find.
After that you'll be able to do a site:example.com "keyword" search to see if pages that had NEVER included the keyword while accessible from the www subdomain had migrated to the non-www one.
I have NO idea why i had to type this all.
Hope it helps.
...no make that i hope it made any sense.