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.
Imagine a pathologically idealistic, anti-religious, culturally-relativistic, iconoclastic, socially-irreverent, sociologically-progressive signature line here. Or don't.