The jury didn't proclaim Casey Anthony innocent of murder. They proclaimed that the evidence submitted did not prove it. That's the job of a jury.
My experience serving on murder trials as a juror is that there is more to any case than meets the eye of what the public is privy to. I think our legal system, although not perfect, is the best possible under our laws.
The only suggestion I could make to possibly make it even better would be to have "professional jurors."
On one case I was on, one of the jurors said the person was guilty. She just knew it and when asked of what evidence convinced her, she said it was "womens intuition."
On another case, one of the jurors said he would vote either way as he wanted to simply go home to his girl friend.