I bought a refurb'd MacBook from apple.com. It's been great. But now I have a minor support issue and noticed that the serial number on the MacBook (About this Mac) is different than the one on the invoice. Doh! Seems like someone packed the wrong MacBook in the wrong box when I bought it. Of course, AppleCare can't help me until I get this situation rectified with Sales Support.
Apple often changes the serial numbers on computers when the refurbish them. Unfortunately, it's been known to cause problems when warranty issues arise.