On the character select screen, rapidly moving ↑ & ↓ starts shaking the screen, and the characters will react to it.
Advancing cutscenes with the combination of ↓ and C (in the Wii U version ↓ & X) will trigger bloopers (selected cutscenes only).
Having a total of four save files of the same character used will cause other save files to have different expressions of the shown character including a Derpy Lilac from the Alpha version from 2013.
When playing as Torque, on the weapon select screen, holding down ↑ and pressing ↵ Enter on ready triggers a hidden start animation of Torque screaming "here we GOOOOOOOOO!" while his neck extends upwards.