For me, there are 3 things that I would tweak when it comes to the coaches challenge:
1) Coaches shouldn't be afforded any amount of time to decide whether or not they want to challenge a play. Seems like after every goal, it takes two minutes for them to drop the damn puck. If you can't tell with your naked eye that a call was wrong, it shouldn't be challenged.
2) Once the play is challenged, refs/linesmen should be given 1 or 2 looks at the play. If you can't tell after a couple looks if your call was wrong, then the call stands and let's move on with our lives.
3) Increase the "penalty" for an incorrect challenge. Right now, a coach simply loses his timeout if a challenge is incorrect. I would be in favor of a delay of game penalty. This would deter the "killing of momentum" during a challenge.
Basically, my point is that challenges should be reserved for the blatant missed calls (the Marchand play at MSG late in the season comes to mind).