1. Games with an excessive amount of fighting, for example the Penguins vs. Islanders 2011... 65 total penalties including 15 fighting majors, 21 game misconducts totaling 346 Penalty minutes. This exemplifies everything that is wrong and barbaric about this game, and also a great example of how fighting doesn't solve dirty hits.
2. Fans who cannot appreciate opposing teams' good players, particularly star players. I get so irritated when I hear fellow Penguins fans say stupid things like "Ovechkin isn't even that good, he just stands there and takes one-timers", in the same way it's irritating to see fans of other teams trying to discredit Crosby just because he plays for their rival.
3. Fans who talk about the players all night long, especially when they have particularly targeted criticism toward one player. At Penguins games it tends to be targeting Malkin, Fleury, and Murray. This is especially annoying when it's obvious they don't really know what they're talking about.
4. Officials skating past broken sticks or dropped gear on the ice and not picking it up. I swear I recall officials picking up broken sticks a lot more frequently in the past than they do now.
5. The obsession with using advanced statistics and thinking that punching out formulas all day is a substitute for actually watching the games or understanding how the human element to the game affects it.
Edit:
6. Players being forced to fight after a hit. Fighting is supposedly this way to police the game and keep dirty plays out of the game, and yet it's used so frequently after a perfectly okay body check.