There's been enough written and spoken about this case over the past few years. We all know that Peterson was convicted and sentenced to death for the murder of his wife Laci, and his unborn son (subsequently named Conor.) There's a new wrinkle, which may give grounds for an appeal (which is automatic due to Peterson's death sentence anyway.) It seems that star witness Amber Frey was collecting child support for four years from a man named Anthony Flores, who DNA tests have now revealed is not the father of her daughter Ayanna. More here.
In my opinion, Ms. Frey is a consummate liar (she called Flores a "deadbeat daddy" when he fell behind in child support, probably with full knowledge that he was not the child's father at all.) This puts her entire testimony in the Peterson case in question, and leaves a lot of ground for appeal. Not that I think Peterson's innocent, though. But, fair is fair, and if she lied about who the father of her daughter is, what else might she have lied about?

The problem is that Appeals work only on matters of law, not fact.

Agreed. I guess I watch way too much Law & Order these days. Peterson's lawyers would have to prove Frey perjured herself. That may be difficult, being that she recorded many of the conversations she had with Peterson. If the facts about the father of her first child (she has two) came out during the trial, that might have swung the jury more in Peterson's favor, possibly hanging the jury, with the result being a mistrial.
But, at the least, the father of her second child should now have a DNA test. And, I hope Mr. Flores takes Ms. Frey to civil court, to try and recoup some of the back child support he has paid on a kid he did not father.

Moreover, Adam, one has to reason whether her testimony was A. consistent with the rest of the evidence, and B. the sole basis of Peterson's conviction.

Just wait until I take over! Mwa-ha-ha!

Peterson's death sentence has been overturned. However, his double murder conviction stands. More on the louse here.

That's all right, he wasn't likely to be executed anytime soon and he'll cost the state less than if he was still on Death Row