I don't know if the swinging was for realism, but real skaters would not be turning that quickly. Also, good filming will stay on one side of the skater unless the line necessitates that you change, in which case it should be done fairly smoothly.
When you switch to freecams, make sure you pay close attention to framing. (That is--where your skater shows up in each key frame. Regardless of where ever the camera is, it's better to keep the skater in the same "picture." Follow cam does this for you, but it's smack in the middle and pretty boring IMHO.) There's your critique.
pick a side of your skater to film on and stick with it, switch sides only if you need to get a better view or really want to highlight a certain trick from the other side, waving the camera back and forth in between tricks is disorienting and unpleasant.
Try to stay away from follow cameras, they look really weird. And for the stair set at the end try to make the camera angle a less drastic change. I'd suggest using adv. free camera only. Read the tutorial in the OP.