There are two things that drive me crazy about NHL officiating:
1) Inconsistency
2) Game management
Officials are going to get some calls wrong, that's just a fact of life. They're human and the game is crazy fast at ice level.
What I cannot stomach is when a play is a penalty in the first period, but that same play is not a penalty in the third period.
I also loathe "game management". If you have watched the league for any length of time, you can predict who is going to get the next penalty with a fairly high degree of accuracy. This is just wrong.
In a 5 on 4 situation, the threshold for a penalty on the shorthanded team goes up and the threshold for the team with the man advantage goes down.
In a 5 on 3, unless it's a mandatory call like a puck going over the glass, there is no way in hell that the shorthanded team is ever getting another penalty. Meanwhile, the power play team will get a penalty if they even sneeze on an opponent.
If one team gets 3 penalties in a row, you just know the next call is going against the other team.
I'm sure there are other cases, but these are just the ones off the top of my head.