Shifting harshness and shuddering issues related to the operation of the automatic transmission have been addressed by factory service bulletins. The shuddering can feel like the vehicle is being driven over rumble strips.
Problems for specific Dodge Grand Caravan years:
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Repairpal verified 2013 Dodge Grand Caravan problems
A problem with the sliding door track and door stops can allow the door to slide out of the track and fall off the vehicle. This is more common when doors are opened fast and allowed to hit the stops with a lot of force.
The auxiliary heater hose connections (that are routed to the rear heater under the vehicle) can develop coolant leaks.