Like his velvet waistcoat, the 11th Doctor’s “anniversary” waistcoat had six buttons.
These buttons were dark, approximately ⅝”, four-hole buttons, with a ring of white dashes outside the holes.
These buttons weren’t strictly cylindrical; the underside was slightly wider than the top.
The buttons appear to have been evenly spaced, vertically, and approximately 2 ½” apart (measured from center button to center button, or from buttonhole to buttonhole).
At a glance, the buttons appear to have been aligned, vertically.
However, upon closer inspection, we can see that the lower five buttons appear to have been horizontally positioned so their outer edges were flush with the vertical edge of the plaid at the center.
That said, remember how the upper front of the waistcoat was gently curved?
This necessitated the top button (or possibly even the top two buttons) be slightly offset from center.
This was most easily observable in the scene below, when the waistcoat was apparently buttoned but not pulled taut at the top … the damn holo-projector must’ve been malfunctioning!
Also, if you look closely below and use the vertical stripes of the plaid as a reference, you can clearly see that the top button was positioned slightly outward relative to the others.
This doesn’t appear to have been universal (because of course); remember the “anniversary” waistcoat Peter Capaldi wore, with the less-curved upper front?
On that waistcoat, the top button doesn’t appear to be offset much – barely at all, really.
And if we assume the buttons were pulled taut to the ends of the buttonholes, the top two buttons both look slightly offset from the rest!
In any event, the buttonholes were “keyhole” buttonholes, sewn with purple thread.