Free Kick: Finish the story on Hard mode to get the Free Kick ability, which allows you to defeat any enemy in a single blow (except for the Arachnina, which requires 2).
Control the paw prints: You can control the direction of the loading screen's paw prints with the control stick.
House gag: In the very beginning of Episode 1, go left and press the action button in front of Crash's house to go inside and hear something random.
Credits Commentary: To hear the game's characters commenting on each person's message in the credits, just press the jump button when prompted.