I provisioned several hundred x220's for the school I was working at, figuring they were the most bomb-proof thing at the time. The lid section you're talking about was definitively not bomb-proof. Thankfully, it didn't make much difference to the operation of the laptop, but still pretty annoying.
Good to know I wasn't just unlucky.
Did you find any typical repairs for the lid section?
(I haven't opened up my wiggly units yet, but I guess probably it got banged, and either screws were stripped out of their holes, or some internal plastic piece snapped.)