Juries absolutely do make errors, including ones which result in innocent people being put to death.
In a number of cases, the Innocence Project has certainly managed to find hard DNA evidence that linked the actual murderer to the crime, resulting in saving people from death row. One of my friends worked on some of these cases. As former law enforcement, he was very much aware of the various ways the system can fail. Police officers commit perjury on the stand, "expert" witnesses use pseudoscience with zero factual evidence (there are processes to prevent this which have gotten slightly better), and there are shockingly terrible public defenders.
