After the first blog post of Content Type & the Managed Metadata Service I went and checked my content type in the subscription site and discovered a fields missing. It was missing the lookup field.
To help find the cause I went to (Root Site) > Site Actions > Site Settings
Click on the content type publishing error log and you'll see a log of issuse .
To resolve the issuse I tried to export the lookup list by saving it as a list template and moved it to the subscription site. I had some trouble with this so I just recreated the list with the same name and data and IT WORKED. I was surprise because I thought it would not work because usually lookup list field use the GUID to the lookup list. The field and the data came it fine.
To keep the lists in sync there a lot of third party solutions.