I would love to see more moderation in the adversarial system. Make the judge and jury an inquisitor of sorts, empowered to ask directed questions to the parties involved in a lawsuit or criminal case, although in a criminal case the defense doesn't have to answer and can still assert the 5th amendment. A judge, and even the jury itself, should be able to ask questions if they feel there are relevant issues or viewpoints that are not being presented properly to the jury.
“The egg hatched...” “...the egg hatched... and a hundred baby spiders came out...” (blade runner)
“Who are you?” “A friend. I'm here to prevent you from making a mistake.” “You have no idea what I'm doing here, friend.” “In specific terms, no, but I swore an oath to protect the world...” (continuum)
“It's a goal you won't understand until later. Your job is to make sure he doesn't achieve the goal.” (bsg)