if the site is working for both mydomain and www.mydomain, you should force it to the preferred host name, on this site we force it to www but you may choose either with or without www for your site, but you should force one or the other.
for your home page there should already be a canonical url link in the head of the page so google will not see it as a duplicate but you need to specify the preferred canonical in page settings.
ie on this site if you view the source of the home page you will see:
<link rel='canonical' href='http://www.mojoportal.com/' />
and the same canonical is used no matter whether the url has /home because we set it specifically in page settings > SEO > Canonical Url Override.
See the article Optimizing Your Home Page SEO
pages other than the home page generally only have one url so the default canonical should be correct on those
unfortunately tools that scan sites and make such reports may not be aware of canonical links so they may flag problems that don't exist even after you make the correct settings
Hope that helps,