Here's a suggestion for how to build a precise and accurate Nipkow disc using only hand tools.

First I'd build a template, as shown. This template has a 'centre hole' at left side, and this is used to attach the template to the disc one is creating. The attachment would allow rotation of the tool. The template has a centre-line scribed all the way along; this is used for angular alignment with points on the disc (described below). The template also has a pre-drilled set of Nipkow holes, spaced as shown... these are used as a guide to drilling our holes in exactly the correct horizontal spacing.

After our disc has had the angular marks prepared (see below), the template is locked such that the Nipkow holes in the tool always describe the correct relative (side by side) position of the holes. Once the tool is rotated to the correct angle, the correct template hole is chosen as a guide to drill the Nipkow hole underneath.

What remains to do, then, is to determine the correct rotation. Since we are dealing with 32 holes/rotation, the disc needs to be divided into 32 equal sections. First I'd draw line across the whole disc going through the centrepoint. Then I'd measure from the edge of the disc on the line, 45 degrees to find the right-angled crossing. Since it's a triangle with equal sides (the radius), the distance expected would be sqrt(2) * radius. I'd measure from both sides and make sure the point I chose was equidistant from both -- doing this for both hemispheres of the circle gives us our right-angled points. Mark them both. Now we just need to successively divide each section by halving the distance between each point and the other forming that section. For example, with the 4-pie configuration we have after doing our initial measurement, we measure from the circumference point to point, divide that in two, and put a mark on the disc. Do that for opposite hemispheres, just for sanity/accuracy, and a line from these two points through the centre.. should be coincident with the points and the centre. If not, re-measure. Once you've got an accurate line, you have two more points to put on your circumference. Repeat until you have 32 divisions. The first iteration you have 4, the second you have 8... then 16.. then 32.

After marking the 32 points on the circumference of the circle, then you drill the centrepoint in the disc (same diameter hole as in the tool centrepoint hole). Attach the tool to the disc via a pin that allows rotation (the drill bit will do, in a pinch). Now align the scribed midline on the tool with a point on the circumference on the disc. Choose the appropriate Nipkow hole on the tool (you step one per marking, of course), insert the Nipkow-size hole drill bit into the template, and drill through the disc. Also do the synch hole for 31 of the 32 'lines'. Repeat for 32 scan holes, 31 synch holes.

Of course I haven't done this, but this seems to me a good way of building an accurate disc using just a ruler, a hand drill, and no need to measure angles at all.

The nice bit is that all the ruler-based measurements are dividing into equal halves, also with mirror images on the other hemisphere of the disc. Your line from point to opposite point should always pass through the centre. So you can always tell exactly when your measurement is incorrect.