88 528e tach not working & bad vibration when moving

I AM NEW TO THE BMW GROUP AND HAVE JUST GOT THIS 1988 528E W 146K MILES. VARY NICE CAR BUT IT VIBRATES WHEN MOVEING MOSTLY ON TAKE OFF A FEW TIMES IT FELT LIKE THE DIVELINE WAS HITTING THE UNDERSIDE OF FLOOR ALSO THE TACH
DOSE NOT WORK & THE HEETING IS NOT THAT GOOD. IT IS AN AUTOMATIC BY THE WAY. CAN ANYONE PLEASE HELP WITH ANY OF THESE PROBS?
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Bad tacho is probably due to dead SI (service indicator) batteries. They are AA size NICADs with solder tags and live right behind the green service LEDs. You must charge them before installation. This fixed a bad tacho on my eta.
Vibration could be a bad driveshaft centre bearing or diff mount.
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