Highlight the prepations made to conceal the body as well as Casey's demonstrable status ad a chronic liar, regarding her ever shifting and changing story ("We're you lying then or are you lying now, what IS the truth, Miss Anthony, do YOU even know?")
In essance you have to completly discredit her and anything she might allege and proceed on the facts in evidence. this will, I believe reveal her actions as an act of deliberate murder in cold blood of her child and put her i nthe electric chair.
She didn't take the stand, and so wasn't available to be crucified under cross-examination.
The state's attorneys did do a pretty good job of showing that she was a liar. They didn't prove beyond the jury's doubt that the child was murdered, and by her.
The guy who apparently found the child notified the police of his discovery
four months before they actually located her remains. Wikipedia says that he tried to contact the sheriff's office on three successive days before they called him back, and then the sheriff's office claimed to have sent a car to search for the scene described which found nothing. It was not until the meter reader contacted the police
again, four months later, that they located what he had described. If they'd actually sent a CSI team to where he was standing, while he was on the phone, the forensic evidence might have been less degraded and perhaps more compelling.
Had the state's attorney sought a lesser charge - manslaughter, or reckless endangerment, say - the jury might have convicted. But going for a capital sentence for a murder one charge in what the state's attorney himself called a "dry-bones case" was always an uphill struggle.