A trial by a jury of peers is, to date, the best method of determining a person's guilt or innocence. I also appreciate the US ideal of assuming innocence until guilt is proven beyond a reasonable doubt. In some countries, it is assumed the person is guilty unless proven innocent (especially among dictators).
What I don't like is that, as with any democracy, things eventually degrade into a plutocracy - those with the most money run the show. Some would argue against this, pointing to rich people who have been imprisoned. However, it is the rich who finance campaigns, and so the elected officials then cater to the rich who supported them.
I also think that a jury should be able to hand down the sentence, especially in cases of potential capital punishment. Many times, the jury will hand down the verdict, but then the judge delivers the sentence. I disagree with laws providing minimum and maximum sentences in terms of fines or prison sentences. Instead, I think that the jury should be able to deliver whatever sentence they find reasonable for the offence. Of course, the sentence would then be subject to the appellate court, where the prosecuted could contest evidence.