This is the WordPress.com support forum where we provide support only for free hosted WordPress.com blogs. if you have not et registered and account at WordPress.org then do so on the top right hand corner of this page http:// wordpress.org
If you did not purchase a domain mapping upgrade form WordPress.com prior to moving your blog then broken links are the result. If you did purchase a domain mapping upgrade from WordPress.com then you need to update the name servers.
The reason we purchase domain mapping is so that all the URLs from the .wordpress.com root blog when clicked seamlessly redirect to the same content in the post under the new domain URLs.
The pagerank and authority the blog earned was earned by the .wordpress.com URLs and belongs to them. It’s not transferable. so what that means is the domain starts from zero. In about 4 – 6 months time the content will all be re-indexed by search engines under the domain URLs and all things being equal the blog will probably have the same pagerank and authority it had prior to purchasing domain mapping. http://en.support.wordpress.com/domain-mapping/register-domain/
If you do not renew your domain mapping then all those domain URL’s are broken and the blog reverts to the old .wordpress.com URLs. Then all those broken links are there for months until the search engines like Google index them again under the .wordpress.com URLs and clear their caches (3 – 6 months).