Peterson's arraignment was postponed Friday when neither of his lawyers showed up in court.
Savio's body was found in a dry bathtub in her home in February 2004. Though originally ruled an accident, the probe of her death was reopened and her body exhumed after Peterson's next wife, Stacy Peterson, vanished into thin air a year and a half ago.
Peterson maintains he's done nothing wrong.
And even in manacles Friday, he maintained a certain swagger and a sense that he's worried about nothing, observed CBS News correspondent Dean Reynolds, joking about his prison jumpsuit and referring to his handcuffs as "bling."
But, notes Reynolds, prosecutors seeking a conviction may use a brand new law - one enacted specifically for this case - that would allow potentially damning statements from either Savio or Stacy Peterson to be used as evidence.
Will that and other evidence authorities say they have against Peterson be enough to get a conviction?
The question was put to a panel of experts on The Early Show Saturday Edition by co-anchor Erica Hill. It was discussed by CBS News legal analyst and former trial lawyer Lisa Bloom, CBS News legal analyst and criminal defense attorney Mickey Sherman (author of "How Can You Defend Those People?"), and Dr. Lawrence Kobilinsky, a professor of forensic science at John Jay College of Criminal Justice.
Pointing to the three-year gap between when Savio died and her body was exhumed, Hill asked Kobilinsky whether authorities could obtain any new evidence at that point.
"Apparently she was buried in a low-cost casket that wasn't really effectively sealed," Kobilinsky responded. "That is, there was water leakage. And of course, as time goes by, there's more and more decomposition. I'm not sure whether she was embalmed or not. That would have retarded the decomposition, but it still would have taken place and information would have been lost.
"I think what happened in the subsequent autopsies is they learned a little more than the first autopsy, but they were highly reliant upon the finding of drowning. I think there's no question she drowned. The question is, was it an accidental drowning or was she forced under the water?"
Her hair was soaked in blood, Hill noted.
Bloom said the new law that may be used against Peterson could play a role.
"In November '08," Bloom explained, "Illinois passed a law allowing murder victims to speak from the grave. Essentially, what they're going to do is (seek to) allow (into evidence) Kathleen Savio's statement to her sister, 'If anything happens to me, Drew killed me.' In a letter she wrote to a prosecutor, she said, 'He will do anything to get custody of the kids, including kill me.' Those statements may come in(to evidence) under the new law, notwithstanding the fact that they are hearsay - they would ordinarily be kept out - the idea being that a jury should hear that, let them decide the weight to give it, but they should hear it, that should be a piece of information they know."
Sherman described the way a defense attorney would go after such evidence, saying, "You've got to keep that statement out. It's inherently unreliable. That's why you have hearsay rules. And what about the Sixth Amendment? You're allowed, you're supposed to confront the witnesses against you. It totally takes that out of the picture when you just put these statements in. Plus, it's to somebody else. The letter. The statement to her sister, you know, again, it's not even firsthand."
Hill wondered whether Peterson's demeanor up to now could hurt him, though his lawyers say joking and wisecracking are his way of dealing with stress. "For a lot of people," Hill observed, "from the time his fourth wife disappeared, it's been seen as insensitive."
"It's appropriate conduct if you're the host of 'Hollywood Squares,' Sherman said. " ... His apparent infatuation with the media -- it's just such the wrong way to go. It's inappropriate. It's creepy. ... It could very well be his downfall. It's an attack on his character that he's engineered himself."
Bloom said the accusations involving Savio may not be all Peterson has to deal with.
"I'm expecting that charges may be filed with regard to Stacy, as well," Bloom speculated. "The grand jury is still convened. They're meeting every Thursday, as they have for the last 18 months. They have a few weeks left in session. He gave an interview recently on a local radio station where he was asked, 'What do you tell your kids about Stacy's disappearance?' And he said, "I tell them she's gone and she's not coming back.' And the reporter said, 'You say she's not coming back?' And he says, 'I didn't say that.' That's all caught on tape. He very clearly did say that. He's made a lot of statements, he's done a lot of interviews. I've interviewed him. That's all going to be poured over by prosecutors for inconsistencies. Mickey, I'm sure if he were your client you would not have allowed him to speak as much."
Sherman readily agreed.
With all that having been said, the panel seemed to be leaning toward the odds favoring an acquittal.
Asked for a prediction, Bloom said, "It's a little too early to say. We have to watch the trial unfold."
Kobilinsky replied, "The key is reasonable doubt. If they can convince the jury of reasonable doubt, he's free."
Sherman -- the defense lawyer -- was most definitive, saying he doesn't expect a conviction "from what I've seen so far." But he added that the public hasn't seen all the evidence against Peterson, because "the police ... are keeping their cards to themselves, as well they should."