Tonight the answer revealed itself. It seems that the blue- or green- (whichever colour it is) screen (is it called chromakey or something?), that the presenter stands in front of, is made up of about nine large squares (like tiles) on the wall. Tonight the joins of all the tiles were showing like a large grid of fine black lines on the screen. The four small black squares previously-discussed are clearly at corner joins where four tiles meet. So the cause of the squares seems to be imperfect joining at the corners of the tiles.
My curiousity is satisfied. Anyone else see this?