You should check out this New Yorker story on Cameron Todd Willingham. Especially if, like me, you are a death penalty supporter. The story didn't change my mind on the issue - I think some crimes are just so heinous we must have the ultimate penalty.
That said, it should be really hard to execute someone. For instance, you shouldn't be able to do so with just eyewitness evidence. Also, someone in a death penalty conviction should have every opportunity to appeal their case. This should be something that's hard to do and states like Texas make it way too easy, relatively speaking.
Anyways, give the article a read.