Bravo
Looking back from the first flash you submitted, and I reviewed, I can tell that you have really improved.
Still not perfect, or even good enough, but I can tell you are really trying to improve.
This I applaud.
I can see you used random movement on the music signs in the background, that is very good.
I like how you made the camera follow you.
You should read more tutorials on making platformers, since I felt it needed to be more fluid. I don't like the way the player warps from one platform to another.
I saw some good use of variables to control things like speed, and jump height(jumping is a difficult thing to do in AS3, good job) from level to level, but I would like to see you changing these variables from WITHING the levels.
For example, put pickup items such as health, or running shoes, to make the player faster.
The background bad.
It looks like oval objects with a full palate gradient.
Try to do the same thing, but don't use the gray outline or border for the circles, just the gradient.
That should make it look better, though ideally you want to make a bunch of empty objects that randomly change colors. But that is a bit hard, so this is good for now.
Another bad mistake I noticed was that the music ends, and does not loop.
The music should look for as long as the player plays, it got a bit boring after the song ended in level 3, and I had to play the rest of the game in silence.
Try to see if you can make the obstacles move to the beat of the song, or use something like the winamp visualizer flash API to make the obstacles, or background, move to the beat of the song. Much like in the newgrounds audio portal.
Here is a site that can really of help you with that:
http://www.communitymx.com/content/ar ticle.cfm?cid=8E9A0
(I hope I can post link)
Another thing you can do is try to get music from the newgrounds audio portal to stream into your game(I think NG has an API for that, or I might be mistaken).
I don't really like the song you picked, which is why I think it would be nice to be able to pick our own song.
Just some ideas for your next project.
Like I've said before, keep practicing and practicing, you ARE improving.
Can't wait to see what you do next.