wobble
 

Today while driving (accelerating onto freeway) the car W124 E300D started to shake side to side like its going to fall apart, I could not reproduce the fault at any situation and drove smoothly. Checked the D shaft flex joints and they look good - the centre bearing looks ok too.

I did refill a rear tire to full 28 psi - it was near 15psi when the incident happened.

Wobbles can be attributed to tyres, thought I had all sorts of problems till I replaced the two front tyres on my 450 SEL.

Have a good look at each tire. A defect in a tire can cause lots of vibration, shaking, or pulling.

tyres are nearly new, I think it was caused by the low pressure on one tyre

X2
You could have a bubble in the tread from delaminated belts.
Why was the tire so low on pressure? Probably the same reason as the wobble.

it could take less than one day to damage a tire if driven in a low pressure condition. they generate MASSIVE heat into the rubber and damage is very quickly peaked. especially when it's a front tire. have the low tire examined by a tire shop, preferably the shop that installed the tire, perhaps they can get you a replacement for free.