Death Penalty: when is it right or wrong?

To my mind death penalty is not completely from one or another side. I have two different opinions about it, depending on the case we're facing, so I can maybe say I agree and disagree at the same time.

In 2009, countries like China, Iran, Iraq, United States, Yemen, Saudi Arabia, etc. have applied executions several times (In the United States doesn't apply for all states), and currently, there are 58 countries that practice it.

I had heard on the radio that in the US, a few years ago, a man (dad) was blamed for burning down his house with his kids inside. "Fire experts" determined that he was guilty for doing it, and he appealed the case as long as he could, but they put him to death. They later found evidence that would have exonerated him, meaning that they had killed an innocent man. This is one special case in which I wouldn't agree with death penalty. There are some many processes involved that a mistake on following the case can mean as much as the crime commited. This would also be unfair by not being accurate with the case investigated, and in the same direction it'd cause somebody's death. It seems to me that it could be way too harsh on people, and deciding whether that person is guilty or not can become a long and senseless process (regarding this special case, I mean).

On the other hand, I have an economic argument: I think that if somebody is found guilty, and then she/he goes to jail, it'd cost more money to keep them there for the rest of their lives than actually applying death penalty, which it'd cost less in the short term, and it'd take the problem away from its roots. A bad thing about this is when somebody is killed by another person, and the killer doesn't have a chance to regret, reflex, and think over about what has been done. To be honest, not everyone is going to do that, but if somebody killed in a desperate moment, without thinking about it, but being aware of his "normal personality," it could maybe work somehow.

Now, the question would be: when do we have a right to decide who lives or not?

A very controversial question, because many people say we're not God to decide over other people's lives. But what happens to the people affected by a crime that has been done to a relative for example? We all know what the news show about it. I can see crimes in which relatives are angry and upset about a friend or relative being killed when it's completely unfair. And it's true, they feel helplessness about the situation. Here's when I think in some cases it should be applied. To give another example, I can also mention the times when a person has commited the same crime over and over, and absolutely nothing has been done to stop it. He/She goes out of jail easily, and keeps doing the same. It maybe a case in which either the murderer has mental problems, or he/she is normal and responsible for his/her acts, but in both ways, I believe that the person should be analyzed in order to decide if it should be applied or not.

So, my opinions vary one to another. I wanted to write that I do make exceptions to this topic, but it all depends on the effectiveness and truth facts about the case. Unfortunately, in terms of justice is hard to decide what it should be done because it's always the hardest part to know the complete truth about the situation.