It's important that when you watch, you're not just watching, you're observing. This can be effective when you're especially playing against someone. I watched a video between ZeRo and Ally. I saw some things Ally was doing, such as dashing away and then turning around. He even air-dodged onto the stage, allowing ZeRo to punish him. I found it odd that a professional player would do something a novice would do.
When you watch, you need to keep yourself conscious and aware of what's going on. It's easy to fall into auto-piloting or mind wandering because humans do it nearly half the time. The way to beat this is by being mindful, and I'm going to tell you, it's not easy. Focus on your breathing right now and see how long you can focus on your breathing alone before your mind goes on doing something else. You can catch yourself not focusing, which will demonstrate auto-piloting.
This is easy to do when you're playing against someone or watching a video to analyze what's going on. When you can learn to live in the present, when you focus on what you're doing incorrectly and what your opponent is doing incorrectly, you can learn to correct your errors while avoiding the positive things your opponent does against you while taking advantage of the errors your opponent commits. You don't need to be a yogi in order to analyze a video, but you can start by getting a sheet of paper or a notebook and noting your errors and the good things you did and doing the same toward your opponent.
The way I do it is I focus on the character I was using and keep track of the good and bad. Keep the good, get rid of the bad. Then after the entire video has been played through, I play it again and watch what my opponent is doing. This has helped me improve, but I admit I haven't been doing it often lately, even though I should. Keep trying. It takes practice and the more you do it, the better you'll get.