Hi Bernd,
No nothing like that, it cuts really smoothly, just leaves a faint impression of the lead screw thread mirrored on the work.
I decided to have a better look today to see if I could improve things.
First I put a dial gauge on the bed and measured the carriageway as it was powered up and down the lathe.
To my horror I saw the carriage lifting up and down by 2 thou over it's whole length
So off came the leadscrew and stuck it in the bigger lathe for further measuring

Between the leadscrew section and the bearing surface I measured 22 thou off center !! You could see it clearly going up and down as the lathe was turned by hand.
The tail end was fine, or at least better at 2 thou.
So what to do, buy another? Would that be just as bad............but then I thought what could I do with this one I already had? I mean, not much to loose was there.
So I attacked it and did this, pic's should explain, I had some sintered bearings from another project.
Truing the bearing area of the shaft and reducing it to fit some bearing I had.

Here I'm reducing the outside diameter of the bearing to fit into the mini lathes pillow block.

Installing the bearings, I had to use two, one at each end. I used a press as I wanted them tight fitting.

Fully home

Back on the lathe,
Looks good to me....

But did it work...?
Well the carriageway now only moves 1/4 of a thou, not perfect, but a lot better than it was. Certainly can't do any harm can it. Maybe I'll have another look at the tail end.
Will put it to the test shortly and see if the end result improves....
Regards
Darren