One of our church leagues around here also uses a net.. If a batter hits the net its an automatic out.. and if someone is throwing the ball home or something and hits it... its a dead ball.
So if you have a play at home and you hit the net, what happens to the runner? Does he have to go back to third or take home? Either way, it seems like a huge disadvantage for one of the teams. I think it's a lame idea.