2000 Lexus RX 300 Drive light & headlights flicker &

Symptoms:
1) The clock goes back to 1 pm each morning. This has been happening since February;
2) About 3 months ago, the transmission went out. I took it to 4 places and they all said I need to rebuild mine or buy a used one. I bought a used one from a 2003 and it was swapped out.
3) NOW. Sometimes when I'm driving, the green drive light (the letter D that appears near the speedometer on the dashboard panel) starts flickering. It doesn't go out completely, but it flickers. If it is night time, I can also see that the headlights are flickering.
Whenever this happens, the car starts to shift really rough. The car kind of stutters and jerks. It doesn't stall or anything, and it does shift, but it just feels wrong. If I were in a manual transmission car, it would be as though I'd let the clutch out too soon during a shift.

I took it to the Lexus dealer, explained these issues. They were totally lost. They focused on examining the transmission. They said they adjusted the neutral safety switch, charged me $300 and sent me on my way. Needless to say the problem did not go away and I am reluctant to go back since they looked at me like I was nuts when I described the issue. I have had the car for 3 years and I KNOW something is not right. But what IS it?