Everyone has a few gripes with some of the rules within the NHL. Some almost everyone agrees on, some are more controversial, and some even have almost no support. Still these are all things that I feel should be changed in the league (in order of how much they annoy me).
#1 - Puck over the glass
This rule is really annoying, and furthermore may have cost the Sabres the cup in 2006. The fact of the matter is that the vast majority of the time the puck goes over the glass it is a simple mistake, and not an attempt to "delay the game" or anything like that. So in addition to the fact that the team has already just messed up a clear under the current system they also get penalized as if they had just elbowed someone in the head. Additionally if the game has broken down to the point where the refs have stopped calling almost all the penalties, they will still feel compelled to call this one as it isn't really much of a judgment call. If you want to still prevent the team from bailing themselves out of trouble, treat it like an iceing where the defensive team is not allowed to change their lines.
#2 - Fake overtime
Five minutes of four on four overtime is really just weird. This should really be played five on five, and should go at least ten minutes, so that the teams actually have a chance to score. While we don't want ties, we don't really want games to be decided based upon a glorified skills competition either. Personally I would love if they did continuous sudden death like in the playoffs, but can understand why they may not like to do that.
#3 - Three point and two point games
The fact that some games are worth more then others is fundamentally a problem. Additionally it gives added incentive to play for the tie. Under the current system playing a low scoring safe game will give you an average of 1.5 points, while playing a high scoring exciting style will return an average of 1 point. The easiest fix to this would be to make all games worth three points, so that the expected average return would be 1.5 regardless of the style of hockey played.
#4 - Ignored elbows
The way the league currently ignores elbows to the head is very annoying as this is one of the few penalties that often results in injuries. If players are expected to control their stick regardless (high sticking), then we can expect them to do the same with their arms.
#5 - Distinct Kicking Motion
Nobody in the league knows what this phrase means. It changes every single game, and nobody ever has any clue if the goal is going to stand or not. Personally I don't care if they disallow all goals off of skates or allow them, but the current system of counting them sometimes is really annoying. If they feel that goalies need to be protected from skateblades, they can add a separate "kicking at the goalie" or "kicking in the crease" penalty that has nothing to do with goals, but is instead based upon goaltender safety.
#6 - Rewards for bleeding
A high stick gives a two minute penalty, but it becomes a four minute penalty if the player hit is bleeding. However, this doesn't make much sense as the reason for a player bleeding often has more to do with how tough his skin is or if he has been in a fight earlier, then it has to do with how hard they were hit with the high stick.
#7 - Only three shooters in the shootout
One of the complaints about the shootout is that only four players on the team of twenty are involved at all. This could be easily increased to six players by simply having each side take five shots. Every other sport that has shootouts (Soccer, Water polo, and Handball) all use five shooters a side, hockey should as well.
#8 - No tv timeouts in OT
There are currently no tv timeouts in OT. While this does help the games end a little earlier, this also wears out players and results in lower quality hockey. Also it helps the networks financially, and perhaps would make them less likely to cut away to show horsey races.
#9 - Exception to offsides rule
This doesn't happen often at all, but if the defending team puts the puck over the blueline, all offsides rules suddenly do not apply. The instances in which this is a problem are very rare, but this rule just does not make sense.
#10 - Stay in the box
I'm am sure this will never go in effect, but I think it would be really cool. If a player is in the penalty box at the end of a period, they will have to stay there until the penalty is over, and will not be allowed to go to the locker room for intermission. I'm still not sure what we should do with penalties that result with a player in the box at the end of the game, but I am sure we can come up with something.