but I experienced similar symptoms right before I had to get my tranny rebuilt. First, take the shifter apart and clean up the contacts. It's easy and can help eliminate a lot of dumb problems, like the dash indicator appearing and disappearing. Should have an "E" along with "R, N, D", unless you put it into manual mode. Dirty contact may cause the tranny computer to flake a bit and when you turn the car off you get TRANS PROG.
Also, check your tranny fluid level, and if it persist, get a mechanic to check the tranny for codes.
The way your tach is sometimes bouncing inda leads me to believe that your speed sensor (hall effect) is slowly going - also a cause of the TRANS PROG message.
Good luck.
JD