When Sam and Cat first start the camera to find Nona singing, she is the middle of the world "thermometer". However, when Sam messes up the video, Nona just begins her song. Also, they didn't begin recording when Nona sang her song and only started recording when they see the toddlers climbing.
When Cat said that she couldn't fight in front of a baby, Sam could have just turned the child around with the baby's eyes facing the wall. Response: It is also possible she was using that as an excuse to leave.
During the Toddler Climbing match you can see a huge gap between the floor and the first set of rocks, the gap is so large a toddler couldn't be strong enough to pass it.