>>8669991"Illegal connections" are rules LEGO enforces on set designers. These are connections that are hard for children to take apart (such as a transparent 1x1 cone on a transparent rod - warning: near impossible), stretch the piece, causing more wear, and possibly breaking them, or aren't actual matches (Technic brick hole is not at the same height as a 1x1 brick with studs on the sides, though it is very close)