Tempers flare ….
Sure, it may take longer to obtain a search warrant and the criminal will get away with the evidence before the police show up. But if the police really think someone is doing something illegal, how difficult will it be for them to get a small bit of evidence to present to a judge who will then get them the warrant? I believe that no matter whose house the police search, they will find SOMEthing illegal (except mine of course), a taped baseball game, a copy of Lord of the Rings on a burnt CD, cuban cigars, illegal mp3 files, office supplies or that altar for human sacrifice. So if you removed the need for a warrant, people would be fearing a knock on their doors 24 hours a day, because (let´s face it) people are not going to stop being criminal - that´s just communism!
A jury of REAL peers (murderers judging a murderer, drugdealers judging a drugdealer etc.) will never convict anyone, so you´re left with the soccer moms and such. These people may be more easily swayed by retoric and fancy testimonies, so that in the end, they give the verdict to the guy with the flashier presentation. And does anyone really believe that it´s possible to ignore some piece of evidence even after the judge says: “The jury will disregard that comment (or whatever)”? A group of judges would probably be less problematic than a jury of “peers”.
The death penalty will do nothing. The y have the death penalty in many muslim countries for much smaller crimes than murder. They chop peoples hands off for stealing. Have people stopped stealing or murdering? No. Your sense of justice may be greater if a guy gets the chair, though …