An alternative is to sharpen your pencils with a utility knife & sandpaper: it's more versatile and less wasteful than a regular sharpener. For example, you could sharpen it to an edge (like a slotted screwdriver), and turn the pencil once in a while, so that the wearing helps preserving the edge.
I've also dabbled with Islamic patterns recently. Side-note: I've found some high-quality, cheap second-hand compass sets, that used to be used for wood work a few decades ago (not made-in-China).
Indeed the movement of the pencil can matter a lot, as can how good your compasses are. I've found that a bevelled ruler can be better if turned over so that the pencil rests against the bevel. Otherwise you have to take account of the width of the pencil lead and adjust the ruler position to take account of it.
Certainly small errors in line position, length and (especially) angle can have a huge effect over a large diagram that has a lot of symmetries. It's surprising how noticeable even a small error of 0.5 mm between two lines is that should be colinear.