I found new cush rubbers helped in my old 1100. I've never felt the need in either of my 1300s.
If you bear in mind that when you slow down by closing the throttle, the wheel is going to catch up with the drive from the engine. Do it quickly and you will feel the lash. When you accelerate, the engine will begin to drive the wheel - but only after it has taken up the free play in the final drive gearing - again jerking if you do it too quickly. (This is also true of a new bike, but older bikes tend to have more 'lash'.)
This is similar to a bike with a chain which on acceleration has the slack part of the chain at the bottom, and on deceleration, the slack part is at the top. The trick is to make sure that the tight bit is at the top before any rapid acceleration.
I ride with hardly any free play in the throttle cable and I find that this helps - but this comes with a health warning. There has to be enough play to cope with changes in temperature, and there has to be enough so that the engine doesn't rev when turning the handlebars left and right. (They check for that on the MOT in the UK). So I am in the habit of feeling for the amount of play when I get on the bike.
But by far the best way of preventing it from happening is to be aware of what is happening at the rear end and decelerate slowly to allow the wheel to catch up with the drive from the engine, and to accelerate slowly enough to let the engine start to drive the wheel again, before opening the throttle.
Better still, on the twisties and particularly on tight bends, you don't want this jerkiness to happen at all, so don't let the rear wheel speed overtake the engine speed. One way of doing this is to ease off the throttle, but not allow 'engine braking' - ie keep the engine driving the rear wheel, but just not as fast as you were before. Another way is to use the brakes if you need to when you reduce the throttle input. The engine will always be driving the rear wheel and the throttle is then always read to power you through and out of the bend. It requires a bit of thinking ahead to plan where you want to be starting to accelerate - but that is no bad thing.
I always slightly roll on the throttle before a bend - not much, it is simply so that I can feel that the engine is driving the wheel rather than taking up the slack - because I want to know that the power is driving the wheel before I need it to 'balance the lean'. It also helps in making it a more comfortable ride for the pillion, who doesn't care much for bashing helmets.
I've seen a couple of riders fall off at low speeds when they didn't have the power that they expected to have. One started his manoeuvre on a slight downhill, leant in anticipation of the junction ahead, applied the power to balance the bike and fell over. Reason - he'd forgotten to put it into gear !
The other was a too rapid application of power. The take-up of the lash made the bike jerk and this initiated the kangaroo start that many of us will have experienced when first learning to drive a car. He braked to stop it, with the bike a tad away from upright, and couldn't catch the bike as it toppled over.
Always a good idea to make sure that the engine is driving the rear wheel before you need it, I find.
None of which takes away from Larry's comment about the universal joint.