The prosecutor was also snickering, or laughing during the defense closing, which is terrible manners, and very well could have had the jury questioning just how serious the prosecution really was about the whole case.
I think the prosecution should have realized a LONG time ago that they didn't have enough evidence for Capital Murder. They likely WOULD have gotten a conviction on a lesser charge - but they weren't trying for a conviction on a lesser charge - they wanted the death penalty.
And yeah, she probably should have been charged with child abuse, or manslaughter. Problem is, the Jury doesn't make the charges, they only make the verdict. The prosecution simply didn't have enough evidence for capital murder, and they should have tried her on lesser charges.
The jury had the option to convict her of 1st degree, 2nd degree, or aggravated manslaughter - they found her not guilty of all three counts.