Check all grounds. There are few under the dash and under the hood. There may be a couple under the seats. Check the door connections. Everything runs in CANBUS. If something isn't right somewhere, other items will start to have problems.
It may be worth to have a reputable shop run a scan on the JK. It will tell him a lot of interesting stuff. I don't mean a scan for obcdII codes. A scan with a scan tool is what I'm suggesting.