You easily check if it has that problem. My wife drives a Limited, I wasn't scared of the problem as it was nice and clean vehicle.
If you do have a problem, its not too much of a problem to fix if its just the doors that are broken. Have a read of
www.blendorstore.com . From their tech section:
To read the fault codes:
Turn on the ignition switch.
Turn on the AZC system. The temperature settings should be displayed for both sides.
Simultaneously hold down the AC and the Re-Circ buttons.
Then at the same time, turn the driver’s side temperature (Left) control knob to the right (CW) one click. Release the AC and Re-Circ buttons.
The code numbers will display one at a time with a short delay in between.
21 or 53 – Left temperature door travel to small.
22 or 54 – Left temperature door travel to large.
23 or 55 – Right temperature door travel to small.
24 or 56 – Right temperature door travel to large.
All of the above codes indicate a blend door problem. 54-56 are the most common.
If you have a 15 or 47 – Left temperature door not responding, chances are the driver side actuator motor has failed. That motor can easily be changed.
If you have a 16 or 48 – Right temperature door not responding, than chances are the passenger side actuator motor has failed. This motor is very hard to replace as it is in back of the heater box and to replace it you have to remove the dashboard and the HVAC box.
If the actuator motor does not rotate when you turn on the system, that does not mean the motor has failed. The computer shuts off the motor if it makes one revolution with no resistance.
If you have the “temperature door not responding” code, the actuator motor could still be in good working order.
Grand Cherokee tomorrow. I have done the usual goggle search but what should i be looking at, rust spots, common issues, good stuff to look for, bad stuff???
done my engineering apprenticeship around there... 
