Personally I don't think the death penalty is worthwhile. For one thing, it's a very absolute punishment. Once it's done, it's done. If the dead guy was innocent, there's no way to fix it. With the number of innocent people convicted nowadays, it's impossible to say every death penalty handed down was correct and/or justified in its use. That and, from what I can gather, it seems to go against general conceptions of what power a government should have. People don't like the thought of someone they don't know or particularly trust being able to decide if they live or die.
As a punishment for a sex offender? This sounds worse to me. Sex offenders should have the chance for rehabilitation, reform, and a fresh start. Fair enough, if you have the same person repeatedly committing the same crime, then perhaps the death penalty could be justified. In my mind, the only crime you could really justify using the death penalty for is murder, and then only if the person obviously has no intention of reforming and would be a menace to society, or if the murderer was particularly cruel (I'm talking BTK, Ivan Milat kind of cruel) or a serial killer/ mass murderer (Ted Bundy, Zodiac, George Hennard.)