To improve the ASG make it worth something. I remember back when it was still a game with hitting.
To improve the Skills Competition:
Tweak the relay race to make the events flow better.
One-timer target shooting. Not timed, with passers, and the player is allowed to let a certain number of passes go by.
For the timed target shooting, do away with the passers, just a pile of pucks like they had in the relay -- this would also allow them to place the nets in one end (easier for crowd to follow both shooters).
For the trick-shooting competition, let the players to a single trick only, and let them have 3 attempts to put it in. Most of those players barely had one move, none had three (even St. Louis basically had one move with variations)