Flag up, or down?

The offside law is in the news again following all the fuss about the female linesman (sorry, assistant referee) in the recent Wolves-Liverpool game.  What always amazes me is how often TV replays show that the official - male or female - has got it right.  When you look at it, it's pretty well an impossible situation - you need to be looking in two different places at the same time.  You need to know when the ball is passed, which means you need to be looking at the passer, and at precisely the same time you need to know where the person who will receive the ball is, in relation to the defenders, which means you need to be looking at them.  I have heard it said that a lot of linesmen (let's call them that, OK?) rely on hearing the sound of the ball being kicked and keep their eyes on the putative receiver, but even so it's a very difficult thing to do.  And this business of active and non-active players doesn't help....