2003 Wrangler doesn't shift smoothly, especially on inclines

forget the local mechanic and take it to an accredited specialist auto transmission shop
have a proper diagnosis done
indicates a servo/ solenoid problem

get your codes first. as three things in your transmission can go wrong.the pressure sensor.the governor pressure sensor is failing.and your filter in the box very dirty and needing changed .so get the codes first cheaper.

it may be a bad tps ( throttle position sensor ). it causes transmission shift issues, bucking,jerking, idle surging, engine cut off, surge while crusing down highway. if this does not solve problem, it may be a sticking valve body in transmission. have a good day !! for an automatic tranny.

have the code checked to see what trouble code the vehicle is putting out it will tell whats wrong with the vehicle once fixed light will go off

Yep, sounds like its in limp mode

You need to take it back to the shop and they need to adjust the downshift cable going to the transmission. Easy fix. Good luck dont forget to rate.

It should have a plastic clip at the mount. with a screwdriver press in on the side where you can move it one click at a time. This may take many timed before you hit the right place. If it's like the GM style all you need is a flat head screwdriver and slide the cable back or forward.[Slowly]

What year? If it has a transmission shift cable, it may need to be adjusted properly.

It could be lash in the differential which is normal, but it could also be a loose u-joint in the driveshaft. Check the rear driveshaft u-joints.

You just go to the link I attached I'm sure you will get the solution of your problem
MITSUBISHI MONTERO SPORT SERVICE REPAIR MANUAL 1999 2000 2001 2002 DOWNLOAD