Beyond a certain level of performance (not falling and executing mostly well) the scoring and interpretation of gymnastics routines are completely subjective. There is no qualitative way to score the competition - if there was, the judges would all be coming up with the same scores, instead of sometimes wildly varying ones. If he thinks Nastia was better on one event and you think Yang was, that comes down to opinion, there's really no factual way to determine who is right or wrong.
As a very casual spectator of gymnastics and also the diving competition, I found myself constantly confused by the scoring - I couldn't see flaws or significant differences between two performances, but the scores would be quite different for no reason I could see nor the commentators could explain. And you have to think something is wonky when out of two athletes doing two vaults, one lands both and looks pretty good and the other looks good on one but totally screws the landing on the other and still gets a better score...
Just because you can’t see the difference between two performances doesn’t mean it isn’t there. There’s a reason they don’t just pull people off the street and hand them a scorecard – those judges train for years and take difficult tests to qualify to judge at this level, and they know what they’re doing.
As a former gymnast myself, I can say that although there is some leeway in the scoring, it is
not entirely subjective. The judges have to adhere to something called the Code of Points, which is established by the International Gymnastics Federation and tells them what deductions they are allowed to take for what kind of mistakes. Some of these possible deductions given as ranges, so if one judge takes the minimum and another takes the max, that can account for some difference between them. But most of the time they arrive within a tenth or two of each other, which certainly wouldn’t happen if they were just looking at the routine and saying “Eh, that looks like a 9.55 to me.”
They write down every deduction they take, and if someone challenges their decision the scores are subject to review by the competition officials. If they differ too widely, they try to find out where the discrepancy came from – it’s usually because someone missed something that another judge didn’t, and the competition officials will help to determine which interpretation was correct. They can’t post the final score until they reach some kind of agreement about the facts of what happened.
The mistakes that people can commonly identify – falling, wobbling, stumbling on the landing – are important, but they’re not the only thing that affects the score. The judges see a lot that you don’t, and they have to account for that in the scores. For example, the gymnast who has a mostly solid-looking routine might have failed to reach a full split on one of her leaps, or have stalled a little too long between skills that were supposed to be connected. Both of those are hefty deductions that may even lose credit for the skill entirely.
There are very specific requirements for what has to go into a routine, and if something’s missing – something that you might not know unless you were familiar with these requirements – then the routine may not score as highly as one that met all the requirements, no matter how cleanly it was executed.
That’s not to say that some of the gymnastics scoring wasn’t dodgy. As I said, the judges have a bit of wiggle room – a deduction might range from one to three tenths, depending on the severity of the error and the judgment of the officials – and that can add up, if the judges take a particular liking or disliking to a particular athlete or her style. But it’s really not just a matter of opinion, even educated opinion.