In the youtube video I saw, it was mentioned that the accuracy at the center of a 4x8 plywood sheet is +/- 1/64", near the edges of a 4x8 plywood sheet accuracy is reduced to +/- 1/16". Has this been been improved upon?
I would say that is still a pretty good estimate. I find that my accuracy is better than ±1/16th inch (±1.4mm) pretty much everywhere except the far lower left and right corners.
If the accuracy is not great in the far corners then why do we do calibration in those corners?
Because it’s the worst there! The test pattern is designed to test where the machine is the worst…we already know the middle works 
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we do the calibration in the corners because we need to generate the max amount of error to make it easier to measure, so that we can setup the calculations to correct for the errors.
remember, we are asking people to measure with a tape measure (accuracy of ~1/2mm at best) and we are trying to correct for measurement errors that are 1/10 to 1/100 of that.
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so what do you do to compensate for the error? program around it? also, is the error a function of the chain geometry, and couldn’t the firmware be changed to improve the accuracy?
The firmware is being changed to improve the accuracy, but since the error
depends on a lot of things (including the exact weight of the sled), we need to
make some measurements and do some calculations to figure out what the
corrections should be so that the firmware can do the corrections.
This is what the calibration step is doing.
It makes some cuts without applying any correction, then it asks you to make a
couple measurements. It then takes these measurements and plugs it into some
fairly nasty math to calculate what the correction factors should be for your
machine.
If you then to the accuracy benchmark, (which cuts squares in each corner of a
sheet along with a couple other lines), you can see how much error there is in
your machine.
David Lang