The sign outside the school board building indicates that it's the "J. Parizeau English School Board", a deliberately-ludicrous name choice since Jacques Parizeau was a famous Québec sovereigntist, and a supporter of the provincial legislation that restricts access to English-language public schools.
Jay Baruchel's sister, Taylor Baruchel, not only has a supporting role in this film, but shares a birthday with the real Leon Trotsky.
Director Jacob Tierney learned about Leon Trotsky as a child, and became fascinated with the Russian figure and his life.
At one point in the film, Alexandra jokingly inquires if Leon intends to live out Trotsky's life 'icepick and all'. This is a reference to how Leon Trotsky died due to injuries sustained from a blow to his head from an icepick.
One of the students in line for the social justice-themed dance is wearing a René Lévesque mask. Lévesque was the founder of the left-leaning Parti Québécois. He was famously portrayed by editorial cartoonists and satirists as a heavy smoker, so appropriately the student has a cigarette in his mouth.