Howdy, Chuck!
The rear differential issues on the CTS are blown way out of proportion on these forums. There
are an above average number of CTSs that have a "hum" or "whine" noise from the differential at certain speeds, but it's certainly not a sign of failure and definitely nothing to be overly concerned about. Make a few tight turns in a parking lot to be sure there's no clunking or binding in the rear and you should be fine. I'd recommend asking the dealer to drain and refill the differential with fresh synthetic fluid and a bottle of "friction modifier" (all parts departments have it) just to start with fresh fluid back there.
As far as the transmission, I haven't seen too many of those replaced, but cars are made by humans and some just break. As long as the new transmission is acting properly, I'd consider it a bonus (new tranny!
)
Thanks for valuing my advice, and if you have any other questions relating to the car or the purchase then let me know!
