Personally, I also feel that it is morally wrong to give jurors life and death decision making power. The jurors themselves can be deeply harmed by this if they later learn that they convicted a defendant on the basis of false evidence.
I think the bigger problem though is that the death penalty is too abstract. There are many people who believe that certain crimes are worthy of execution. I don't personally agree, but I accept other's beliefs on that point. But even if I grant the righteousness of execution in certain cases, it seems nearly impossible to implement justly and without heavy costs to society. This includes the costs to the people who must carry out the execution as well as the exceedingly high financial costs relative to other forms of punishment.
In practical terms, it also requires an incompetent lawyer. Ruth Bader Ginsberg said "No well defended person receives the death penalty." I read that in an article about the one isolated case where she was wrong.
I also suspect that the death penalty corrupts the societies that use it.