From what you described, I guess that's something about nnedi3, not about this script.
nnedi3 is an edge-directed interpolator, which means it interpolates image guided by edges(line, fine structure, texture, etc.). While in general edi can produce much better results than simple isotropic interpolator such as B-Spline/Lanczos, it will also produce artifacts in some regions such as the ones with complex textures.
As for nsize, nns and pscrn, they are the parameters of nnedi3, so you can look into the readme of it. For example, nsize=0/4 is suitable for upscaling, nsize3/6 is suitable for AA since it connects more lines(as well as produces more artifacts).