The non-calls on clear icings in the third period are really the only things that get to me as a player. The other periods are run-time anyway, so they get called more often.
I don't really care when a referee makes a questionable penalty call because they go both ways and for every questionable call there's also a questionable non-call. I've been sitting on the bench plenty of times remarking to teammates that we really lucked out on a non-call sometimes (usually a trip that doesn't get called). Wrong calls on off-sides, missed high sticks (hitting the puck), and getting in the way occasionally (if it's constant, it's a problem) are all no big deal things to miss.
I think the refs are pretty good in my league; I don't take many penalties, (1 penalty every 9 games) but on all but one penalty my whole time, they were no-doubter accidental trips/high sticks/etc. and I just went to the box. The other was a really soft call, but I still just went to the box. I like being competitive out there was much as anybody, but that doesn't mean you should disrespect the refs. In all of everybody's arguing how often do they actually get a call reversed? :p You're more likely to just add minutes on if you start complaining like a princess. In fact, if you're a princess, you'll probably start getting called more often (particularly if you're a princess and a ringer... poor league management...).
I haven't actually reffed hockey before, but I have reffed soccer quite a bit. In my experience, most people who badmouth referees and complain all the time have never actually held the whistle themselves. At any level in any sport, it's difficult. Little things go on all the time and it's impossible to call everything 100% correct. This is why I agree with the advice that "if you think you've been hooked, tripped, etc, then just keep playing and going for it." After all, in both soccer and hockey, the play doesn't stop until you've lost advantage anyway. Maybe if you kept chasing the puck, you just may have scored.
Remember what your old coaches told you and play to the damn whistle! The ref ain't going to catch everything, so get that illusion out of your head.