I think this subject has been done pretty much already, but I'll throw in my take.
I'm generally against capital punishment, even though at a certain emotional level I can understand and share the desire just to kill certain people who can be reasonably said to deserve it. This is, though, basically a personal point of view regarding whether it's right to kill anyone, and as such I think it's essentially not a point on which argument is fruitful.
But in addition the imperfection of the system and the ambivalence society holds for it make it physically and morally too expensive, I think. While cost should not be the sole factor, society always has to reckon the cost of things when deciding what to do. The ideal of a just society includes more than just what we do with our criminals. Our politicians argue incessantly about the cost of doing the right thing. We cut taxes, labor protection, environmental protection, welfare, food stamps, education funds, everything from health care to road salt, on the basis of their immediate cost, often at the expense of the future. I find it hard to take seriously the argument of any social conservative that expense should not be a factor in this little corner of justice, when other issues of our society are so pervasively tied to their pocketbooks.
Aside from that, though one can argue about whether there is a systemic racial bias in the justice system, and one can, no doubt, argue about acceptable collateral damage when it comes to wrongful conviction and sentencing, I think the moral cost is too high. The alternative to wrongful execution is not, after all, to let them all go free. We will always make mistakes, but acknowledging that seems a poor argument against possible ways to mitigate their fatal consequences.
In addition, I think the argument of deterrence is weak. I think there is a deterrent effect of conviction and punishment up to a point, but there seems to be little evidence that the sort of person who would be deterred from a crime is more deterred by the prospect of execution than they would be by long and harsh imprisonment.
Justice is a complicated subject, and perfection is not possible anywhere, but I think we can apply some inductive approach to it. Aside from moral dudgeon and the hurt feelings of those who crave a certain standard of justice, what are the overall effects on a society? Are places where capital punishment is rife safer, happier, better in any quantifiable way, than those where it has been eliminated?
Even if we set aside issues of cost and fallibility, I think we end up with the fact that execution and the system surrounding it is not just about the individual decision about what to do about individual cases, but a thing a society itself does and is, and as such it comes down to whether you believe it makes the whole social organism better or worse.