Traced vector has sloppy outline

I have used Illustrator to trace a shape for me, but the resulting vector is rendered untidily. It seems like a rendering glitch, as if Illustrator tries to render the shape's outline using a crude polygon.

How can I fix that?
I need illustrator to properly use the specified 0.001pt width, because that's what my laser cutter understands. If I use e.g. 0.005pt line width, the effect is less serious, and with 0.01pt it is even less visible - but not entirely gone.

PS: I tried to search for a solution, but I don't even know what the proper terminology for such an artifact is.