Driving down the road, car switches to gear other than D, as if I hit the paddle shifter. Is this a basic transmission problem or some other? I would have thought if the transmission were slipping, it still would show as "D" in the selector display, but in my case it switches to a gear number. Happened 3 times on a 15 mile trip. Quite alarming.

 

Does it change gear or just the display change

 

It changes gear.

 

I have the following suggestions:
1. Download from this forum the Service manual (the automatic transmission of the V6 model is the same in the 2nd and 3rd generation Outlanders thus, the information is relevant);
2. Follow the procedures underlined in the "A/T DIAGNOSTIC TROUBLESHOOTING STRATEGY" section;
3. It is highly likely that your ECU is throwing diagnostic trouble codes (DTCs). Get a cheap OBD II code reader and read the code(s);
4. Search for the specific DTC in the manual.
5. For the time being disconnect the paddle shifter (the harness is underneath the steering column: see this video at 1:03 or the 5th picture of #906 here. With this you can eliminate or locate the fault of your paddle shifter.
Good luck and report back what you have been able to find.