Award Snub: They still haven't been accepted into the Rock and Roll Hall of Fame. In fact, the first thing Metallica did when they got accepted is to call out the Hall on how incredibly wrong that is. Even Trey Parker said basically "If you don't let them in you're a being a huge dickhead". And that's verbatim. When they appeared on The Colbert Report the first thing Stephen asked them was if their next album would be called "This is Bullshit".
Eddie Trunk also exclaimed "Rock and Roll Hall of Fame, are you kidding me?!" when Alex and Geddy appeared on That Metal Show. The popular opinion seems to be that Rush have been snubbed by the Hall one time too many.
Dork Age: Fans are surprisingly divided on the albums' respective degrees of quality, but Roll the Bones and Test for Echo are generally considered to be the worst.
Fridge Logic/Fridge Brilliance: The Priests of Syrinx obviously can't take "equality, our stock in trade" very seriously if they won't even let other people play guitar.
But that is equality, albeit of a Harrison Bergeron sort. Nobody is allowed to play music because the vast majority of people can't play a note. How dare musical prodigies be prodigies?
High Octane Nightmare Fuel: "Red Sector A". It is about someone trying to survive during the Holocaust. 'Nuff said. In fact, it was inspired when Geddy told the stories his own mother had told him about her time spent in concentration camps. Both of Lee's parents were Holocaust survivors from Poland.
Ho Yay: Tons of it between Alex and Geddy. Tons. Especially in the Dinner with Rush segment from Beyond the Lighted Stage (the documentary on the band) and during Alex and Geddy's apperance on That Metal Show.
Running the Asylum: Nick Raskulinecz, Rush's current producer, is a major fan of their '70s output and is reportedly trying to push them back towards it for their next album.
They Changed It, Now It Sucks: Understandably, they get this a lot, given the high amount of New Sound Albums. Particularly from the period when Lee focused more on the keyboard than bass.
What Do You Mean It Wasn't Made on Drugs?: Averted with the 1975 album Caress of Steel. In the 2010 documentary Rush: Beyond the Lighted Stage: Geddy admits that the three of them were probably very high when they made that one.