Symptoms
The car rolls away after you get out of it. FCA's own wording for the defect: the vehicles "may not adequately warn the driver when driver's door is opened and the vehicle is not in PARK, allowing them to exit the vehicle while the vehicle is still in gear." The consequence line is unusually direct: "drivers thinking that their vehicle's transmission is in the PARK position may be struck by the vehicle and injured if they attempt to get out of the vehicle while the engine is running and the parking brake is not engaged."
Likely cause
The selector itself, and NHTSA said so about the design rather than about a broken part: it "is not intuitive and provides poor tactile and visual feedback to the driver, increasing the potential for unintended gear selection." A monostable lever returns to the same place whatever gear you chose, so the usual two confirmations — where the lever sits, and how far you pushed it — are both absent. FCA changed the design for the 2016 Grand Cherokee.
How should it be checked?
Check the VIN at nhtsa.gov/recalls for 16V-240; the software update is free and does not expire. Then form your own view of the lever, because the recall mitigates the consequence rather than replacing the design — the car still has the same selector afterwards. If you buy one, the habit worth building on day one is the parking brake, every time, before the door opens.
How can you check it yourself?
Sit in it and put it through the gears without moving. Look at where the lever ends up each time — it returns to the same place — and find where the car actually tells you which gear it is in. Then decide whether you would read that display every time, in the rain, with shopping in your hands.
The question to ask the shop
Has recall 16V-240 been completed on this VIN? Has the vehicle ever rolled away or been reported for it? Does the auto-park software the recall installs work — does it engage park when you open the door with the engine running?