The children's jumping contest is like chicken, to see who can come closest to the ground without actually touching. The one boy seems clearly to have won, but then his nose starts to bleed and the older girl points this out. His nose is bleeding because he hit the ground (not because of the mind/body connection). The "your mind makes it real" explanation is only used in the movies to describe how a body outside the matrix starts to bleed internally and shake violently when it is being beaten up in the matrix.  

 The feather is spinning, and the anomaly is that it is doing so in place. 

 The little girl with the displaced shadow who says "i figured this out yesterday" is observing that she can draw pictures with a chalk stick and have the lines appear where her shadow draws them instead of where she draws them. 

 I wish someone would come and do some original research with regards to the way the girl cuts herself on the can in the last scene of the movie. I would really like to know what was going on in Koji Morimoto's head or at least hear some speculation... heh!