I had actually never heard of Casey Anthony until reading Bill James's book Popular Crime a few weeks ago. So, I have nothing to say about the verdict in her case except to make a general observation. As Dave Barry once explained: "the Sixth Amendment states that if you are accused of a crime, you have the right to a trial before a jury of people too stupid to get out of jury duty."
My experience having been on the jury in what should have been an open-and-shut tax fraud case is that 9 out of 12 jurors were too dimwitted to grasp what had happened even after I had explained it to them. Only the Chinese-American accountant understood the situation after I'd explained it to the jury, and the Bulgarian immigrant used car dealer was smart enough to figure it out, but his biases were all on the side of the accused, an Iranian immigrant used car dealer.
Have there ever been any studies of jury performance based on selection rules for the juror pool? For example, I sat around several times at Cook County courthouses waiting to be called, and the evident quality of potential jurors was pretty decent: a lot of guys in business suits reading the WSJ. Among potential jurors in LA County courthouses, however, you have a lot of people sitting around staring blankly. My impression is that this is due to where names were drawn from at the different periods in different places: voter registration roles in Cook County in the 20th Century, Department of Motor Vehicle rolls in Los Angeles County in the 21st Century. There are a lot of opportunities for social sciences studies here, such as natural experiments of the impact when the source of the jury summons gets changed.
In general, however, most Americans don't seem to want to think about just how badly juries often perform.