Had one back in 06-09, and loved it. Granted, I drove it for the first ~40k, as it was leased, but it was a great car. As Stevoone said, diff bushings. I think the 3.6s were spared the plague of the Crankshaft Position Sensor issue that the 3.2Ls had. But radio buttons often chipped on them as well. CadillacOwners.com is a good site to explore before biting the bullet, if you want more info.
www.cadillacfaq.com was a good source for write-ups and such as well.
Good luck. I still love their styling.