I wrote a book about the trial that breaks down the evidence and testimony and explains why she was acquitted. There actually were understandable reasons. I can answer any questions you have :-)
https://www.amazon.com/Everything-didnt-about-Casey-Anthony-ebook/dp/B079WKF7J8/ref=nodl_
I wrote a book explaining why she was acquitted: https://www.amazon.com/dp/B079WKF7J8/ref=cm_sw_r_sms_awdo_t1_vaxREb8JZRFM1_nodl
TLDR: for one thing, the media made it out to be much more open and shut than it actually was (much of the state's evidence was very poor quality), but the answer is George Anthony. This didn't get a lot of press but he's a compulsive liar just like Casey is. So when police went to interview him, he just made a bunch of shit up. INCLUDING, his story about what happened the day Caylee died. So when the prosecution decided to use him as their key witness, they had no problem getting him to testify against his daughter but it was all lies. Look, she may very well be guilty, but what George told the jurors was very easily discredited because he'd already told three versions of every story.
Like for example, he testified that when he found his daughters car he was 100% sure it smelled like human decomp. It sounds like really great evidence when you hear it on Nancy Grace. But what George did next that day is he drove the car home, told his wife the smell was from a rotting pizza (another lie) and he went to work and worked his entire shift without even calling Casey to see if she was ok. But now on the stand he's claiming he was beside himself over the smell.
Clearly he is exaggerating to help the prosecution. The defense also pointed to all of the interviews he gave where he claimed it was trash. The jurors were suspicious as to why he was trying so hard to get his daughter convicted already, but he didn't like being challenged so he pretended like he couldn't understand the questions. This happened every time George got on the stand.
So from the jurors perspective, Cindy left that morning for work leaving Caylee at the home with Casey and George. Caylee died mysteriously and now BOTH of them are lying about what happened. They couldn't rule out George Anthony. That's why she was acquitted.
I wrote a book on the the trial and it explains why she was acquitted. This is a shorter summary I did a few months ago.
I disagree. I think the public just doesn't understand the case. From a strategic standpoint, they did the best they could with the case they were given. It's not that the evidence was so great and the presentation was bad, the evidence itself was the problem. They had very good circumstantial evidence with the 31 days and Casey's behavior. But the rest of their evidence, particularly their physical evidence, was garbage. On the other hand, the defense had a lot going for them, but the the media was so biased for the prosecution that it led us to believe they had nothing.
The real reason Casey was acquitted is that George Anthony (Casey's father) is just as much of a compulsive liar as she is. Everything George told police was a lie. This may simply be an incidental finding, but it's a problem for a couple reasons: first they used him as their key witness and the jurors felt they couldn't trust his memories. But more importantly, he was the other last person to see Caylee alive. Cindy left for work, leaving Caylee with Casey and George. BOTH of them lied to police about what happened. The jurors couldn't rule him out. That's why she was acquitted.