Scientific Linux was designed so that an administrator can easily upgrade their computer between minor releases.
It is not required that administrators upgrade their release, because the security errata will be updated for all releases. But there are often features and/or packages included in later releases that were not available with the earlier releases.
Below is the steps, using yum, to change to the latest 6.x release.
These instructions are for updating between minor releases, such as from 6.0 to 6.1.
yum clean all