As far as I can tell, outside of the one known position in the dead zone, where the little hole is (I assume that's some sort of optical home sensor, IR probably), the whole thing operates as a stepper motor, counting rotations. Once it homes, you move it to position 1 and mark that setting, then position 2, etc. It remembers how many motor rotations that is from the home. It also remembers how many motor rotations (counting up in one direction, down in the other) since it last was at home, which seems to get lost at times, causing the bridge to first go to home then be able to find the set positions - it still has the count of each position from home saved, but it has lost count of how many turns there have been (I wonder if it's something as simple as an overflow - like it happens more often if you always rotate clockwise and rarely ever move counterclockwise or something). At any rate, it is counting motor rotations, so ANY slack in the gear train from the motor down to that drive gear means the table can be off position by that much without another full motor rotation. That shows up in it not being perfectly aligned when coing out a set point counterclockwise but it's perfectly fine clockwise, or vice versa. And of course as noted the internal track must be scrupulously clean, having even just 1 motor rotation not count because the drive gear skipped on a piece of dirt will throw the alignment off by whatever the overall total gear ratio is.
It's sort of like the new low cost CNC machines you can build - they use steppers, 1 turn is say .0001" of travel, so 100 rotations is .01", vs the big expensive machines which have a servo motor to move the axis with a scale that is read by a sensor for absolute position feedback. It's what enables Walthers to sell the turntable (and the transfer table) for the price they do, when a really accurate positioning system alone, like the one from NYRS, costs more than the entire turntable AND electronics from Walthers.
It generally works well enough, if kept clean and never forced by hand, but as previously noted the microcontroller seems sensitive to electrical noise in the power supply so a well filtered clean power source (and this is what makes the DCC one worse, if track power is used to run the whole thing, track power is ANYTHING but clean) is critical to keep it from losing its mind and fogetting all the set points. It's reasonably well manufactured so the gear lash should be within the ability of most HO locos to cross the joint between table and bridge, but it is also mass produced so it certainly is possibly to get a lemon with a bad gear in it or something.
There are really only 2 other options, a different table controlled by a more expensive controller, like the NYRS one, which has an absolute sensor at each stop so there's no guessing where the table is, or a different table with a purely manual control like the real thing, no indexing. If the table is close to the operator and they can clearly see the tracks to line it up, I see nothing wrong with foregoing the expensive electronics and just use a simple DC speed control.
I don't have access to the Walther circuit, so my theory on how it operates is based on observation and the description given in the instructions. I may be way off, but I'm fairly confident I'm close.