I then select "Deploy Objects" from the right click menu of the Project itself. If there are no errors in the metadata, it deploys to the salesforce org correctly.
If there are errors in the object's metadata, the deploy process will return an error that the deployment failed but there are no indications about what failed.
It seems that the Build process is not checking to see if any objects' metadata changed or not when determinining if a build is necessary. However, the Deploy process does seem to determine that the object metadata has changed and it tries to deploy the object (with changes) to the org and throws an error.
I reported this under Help->Report Bug about 10 minutes prior to making this post but didn't copy down the Unique ID, sorry.