"how can you rectify a miscarriage of justice when you've executed the person that was wrongly convicted?"
Very true, but does this mean we're frequently locking up the wrong ones, but it doesn't matter much as we didn't execute them? I'm in favour of execution, but our first step should be to sort out the mess that is the current justice system.
"extremely expensive to execute someone"
Only because it's a lawyers paradise and is stretched out to make the most profit. What appeal can there be if there is clear evidence that you did it? and unless there IS clear evidence you shouldn't be there.
"having the death penalty is not a sign of a civilised society"
We already have a death penalty which our soldiers apply to our enemies. So we have established that it's ok to kill enemies of our society and are fiddling with the details.
"where there is a death penalty there is no reduction in crime"
When you see someone going back to court/prison for the 3rd/4th or 17th time you know for a fact that executing him the first time would have prevented his later crimes.
Personally I'd only have it for cases where it was the 2nd or 3rd conviction. Even if you think someone might be convicted wrongly it's hardly likely that someone is going to be wrongly accused more than once.