Those are some crazy gremlins. I have never experienced something like that by my first thought would be the Body Control Module. I believe it is the computer responsible for things like doors, locks, lights, alarm interface, etc.
I don't know where exactly it's located but I think it is somewhere in the driver side kick panel next to the parking brake pedal.
Check for obvious things like making sure the wiring harness is correctly plugged in or that there isn't some loose ground wire somewhere to the BCM.
POST EDIT: After re-reading your issues, checking the driver door switch like
@
fbksurferjoe
said sounds like a better answer.