So every time you shift across neutral, or into reverse from P it misbehaves. If you start in neutral can you then go into reverse with no problems? Have you tried pausing in neutral before shifting into either Reverse from D or D from reverse? (You've probably tried everything!) Sounds as if something is loose, damp or mucky in the switch, or maybe there is damp in the plug, maybe causing a short across two terminals so it gets two signals at the same time from the shifter. I assume you switch off between moves, and start in Park if you want to reverse and start in neutral if you want to go forward? Annoying if you actually want to do one straight after the other. Other members on here with more electrical knowhow than me will comment if I am talking twaddle!
Last question, have you checked the ATF level? M&S lights can come on if it is low. And do you have really slow moving away from stop when the gearbox is cold? This can be a sign of a mucky filter in the box. Both of these are DIY fixes. Do read up before removing the level plug. If you do it with the engine not running ATF will pii all over you!