My lathe will repeat as close as I can reasonably measure, would say less than 0.005mm
My lathe however has ground high precision ballscrews with  virtually no backlash, has a resolution of 0.000625mm fromr AC servos  and weighs 3 tonne so  its really not a good one to compare yours to.
Hood

Thanks, that's good information though as it tells me I probably can't get mine much better than it is now so I should stop worrying and start making chips! 

As always, thanks for everyone's help and advice.

John.

If turning down to a specified diameter using the wizard, what is a reasonable accuracy to expect?

Actual turned down diameter will only be as accurate as your lathes "complete system" and additionaly accuracy can be related to surface finish when measurements
are taken on the diameter of the piece. Depends on spindle runout, surface finish, etc.
You have what you have.....!

Moving the slide repeatedly backwards and forwards to the same nominal position, what repeatability can be expected?

Depends on the motors / electonics / drives but also on the mechanics of the system ( backlash / ball screw accuracy).
On my converted lathe repeatable backlash is like  .0004 on the Z and even better on the X. The x axis ball screw is a high end ground ball screw.
So in testing using a .0001" indicator or opticaly compared  it's on as compared to Mach's DRO.

but I was wondering about just how repeatable microstepping is

Well, for my engraving machine i could not measure it ie; didn't have enough light at 400x to read the calibrated glass scale with a microscope.
 I have found different steppers will microstep better than others....Russ gave an example from Geco for the reason.
I can however easily split .001 into 10 parts by jogging in .0001" steps. Now remember that my steps per unit is 253000, thus resolution is
.000004" but practicaly the screws ware only calibrated / certified to .000040" acuuracy over the total movement. As noted by others you will find that
there will be no movement and then the stepper will jump to the next postion and the number of steps can vary over one revolution of the motor. Change the motor and
 you will see a difference if you graphed and compared the movements to steps. So not all motors are created equaly.
 Now if you had a pulse counter you may also find out that even the tension of a timing belt can influence your readings as even though the motor turned from a pulse there was no
mechanical movement due to the belt tension. We did some testing and found that Mach / the PC provided the pulses but the drives, belting, motor, etc didn't mecessarily react to them all.
Things are just not perfect......!

And what is people's experience of the accuracy achievable with Mach?

Mach is more accurate than your ability to  measure the movement..........!
If you have a quality system then you will have accuracy.

RICH

Thanks for the comments Rich...all goes I think to confirm that given that I'm using a standard screw rather than a ballscrew I'm probably getting as good as I can expect. 

This was all a bit of a diversion back to the lathe from my main project at the moment which is converting an X1 mill to CNC, so I will stop worrying and get on with the job!  Maybe one day I will return to the lathe and fit ballscrews to that.

Thanks again,

John.

John,
I fogot to mention that I have a Sherline lathe and it has a threaded screw. I was impressed when i checked the screw in that it was quite accurate in lead going both directions. The problem tough was backlash, even though i had the anti backlash attachment for it.
You could only get so much of the backlash out and then it had to be re-adjusted if used frequently. I will also remark that my tool makers microscope has threaded screws along with an anti-backlash setup and it is extremely accurate. Manny movement tables
use screws, but those devices don't see the wear that a running machine machine will produce. Thus a step up would be ball screws and provide for longevity. Since your interested in accuracy, then each component of the mechanical system needs corresponding attention to selection. You ge a lot for your money but pay more as the accuracy of component is upgraded....ball screws are a good example. Try to make your axis have no backalsh or absolutey minimise it along with a nice balll screw and i think for prcatical use you will be happy with your machine.
RICH