BBM: Forgive me if I am misreading, K_Z, but the way you word the bolded sentence makes it seem you misunderstand the term "jury nullification".
Jury nullification has nothing to do with "nullifying" a verdict or doing anything, as a rule, that overturns the verdict.
Jury nullification refers to cases where the jury decides to ignore the law and vote its own prejudices and principles. For example, white juries that acquitted white supremacists who had murdered blacks in the Old South did so because they believed in protecting the Jim Crow system, not because they thought the prosecution failed to prove the guilt of the accused.
In other words, the jury "nullifies" the law. Once it does, getting that verdict overturned is nearly impossible, as I understand it. First, it's hard to prove what was in the mind of jurors. Secondly, the system as a whole is reluctant to overturn juries. Thirdly, there is disagreement among legal scholars as to whether nullification is legal or not: some argue that under our system juries have the absolute right to rule as they choose, law or no law.
Defense attorneys have subtle ways of suggesting the jury ignore the law and "do what's right instead." How much is allowed depends on the judge. If the jury ignores the law and convicts the defendant, there are all sorts of remedies; but the idea of nullification usually comes up when a jury acquits. And then there isn't much that can be done.
(I am not a lawyer. But I have sat through a number of voir dires where the concept was discussed.)