The death penalty should not be legal. There have been many times that people get wrongly convicted. For most people, if they get wrongly convicted, they would probably rather wait a few years, until it is realized that they were wrongfully convicted. There are times when killers escape from prison, and kill more, but not a lot of people can escape prison, and even less are going to go kill. It obviously happens, but how often?
I believe it should be legal, however, the regulations on it should be air tight. There has to be zero deniability that the person absolutely in fact did commit the crime because, like you said, there have been cases where people were wrongfully accused. So, what's the alternative to death penalty? Locking them away for "life". I feel like keeping people locked up for life is a complete waste of both space and tax payers money. If someone commit a crime that heinous, they should be fully prepared for that consequence. However, I will stress one more time that it be tightly regulated and is only enforced if there is absolutely no doubt that the person committed the crime.
How can anyone be 100% sure someone committed the crime? Even if you get a confession, they can still have been threatened. If the death penalty is legal, then threatening to kill the person to confess to the crime (that they didn't commit). They could still be threatened on their family's lives. I know that this is rare, and a little far-fetched, but it is a possibility, and it most likely has happened at some point in time, some where, even if nobody knew about it. Keeping people in prison may cost money, and space, but they are humans too. One of the parts of being human is that we all do make mistakes, and some mistakes are worse than others. You have too live with the mistakes you make, but how can you live with them if your dead? Also, Why do we kill people, who kill people, to show that killing is wrong? (I am not going to credit for this, I found in a picture on Google.). If you kill people, aren't you saying it's OK? This is like "an eye for an eye", but if you apply that to murderers, shouldn't you apply it to thieves too? So would we start saying that you can take whatever you want from a thief? If it is so wrong to do these things, then why would we, and do we sometimes do it too?