It maybe that the prosecution overshot the mark in seeking the death penatly for Casey Anthony. Maybe if the prosecutors just simiply stuck with manslaughter and child neglect charges, which usually gives a sentence of 30 years maximum in prison, they might have won the trial. The jury might have gone with that, believing it to be a reasonable sentence, since the defense kept saying it was and accident that snowballed out of control. Seems like the prosecution was really reaching hard in proving murder, when the evidence they presented was barely enough to prove much of anything. Like the lead prosecutor said at the news conference after the jury verdict, (I'll paraphrase in short) "it was a dry bones case and very hard to prove something when there is very little DNA evidence left to go on", so it was obviously a very difficult case for them.
Also, I think the fact that Casey's parents lied about a few things in trial didn't help the prosecution much. Her mother threw a bomb in thing when she tryed to say that she was the one who did the internet search on chloraform. And the father was trying awfully hard to hide his infidelity on the witness stand, which probably made the jury think that he did have an affair with another witness(can't think of her name right now) and that she did tell the truth about George saying that it was an accident. So with her parents making false statements and trying to hide certain facts like that, it probably gave support to the defense team's statement of a disfunctional family. And the jury probably thought that was why Casey Anthony lied or lies so much, because she learned the act of lying from her parents.