Pengwuino, I've often thought of the idea myself, but coming from a different angle. My beef is not so much with non-professional jurors as with judges and lawyers. This stems from when I was 10 yrs old and I read in the newspaper that a young teenage boy had been beaten by two other lads to within an inch of his life. Ended up spending months in hospital recovering. The two thugs were tried and found guilty, but the judge sentenced them to a mere two weeks community service each. The father of the boy (who was still in hospital) stood up in outrage and was sentenced to six months in prison for contempt of court. This disgusted me (and is the ultimate source of my ongoing moral outrage at... everything ever since) and I have seen nothing in the next 16 years that has changed my opinion of the British judicial system.
I also have a huge chip on my shoulder that a court case is anything other than a presentation and assessment of all the facts. The job of a lawyer is not to present the truth but to manipulate it and people to strengthen their case. This has nothing to do with justice. IMO, the fate of a man or woman should not depend on the relative experience of the prosecuting and defending lawyers.
So I've often thought that both should be done away with a replaced by a professional panel, like the supreme court in the US, which receives evidence, questions witness, and passes verdict and sentence, all by collaboration. It would probably need work as a model court, but I think the basic idea is more condusive to a just judicial system.