Criminal justice systems are hard. They're right up their with the hardest things humanity has to deal with. They deal with ambiguous facts, necessarily inadequate rule systems and with intelligent human actors constantly trying to game the system - what's more the stakes are terrifyingly high, up to and including the life or death of the participants.
Sure, errors tragically occur. But we should really pause before pronouncing --- based on Bayes, blogs and journalists --- that the cursory judgement of a non-profesional who wasn't in the court is superior to the considered judgement of judge and jury made in full cognisance of the likely outcome of conviction after listening to all the evidence including first hand witness testimony.
And no, throwing in an offhand comment about how Occam's razor disproves God and therefore a little logic wielded with "courage and a certain kind of ruthlessness" enables superior thinkers to do better than the hidebound judge and jury (who were probably irrational Christians anyway) doesn't make the argument any more convincing.