In the Night Owl stage, there should be four small "StarFox" signs on the walls of the course, that fall if you crash into them. Ram all four signs, and an Arwing from Star Fox will fly in and drop a power-up.
Pause the game and when the pause animation comes up, press R to make the animation run in slow motion. Press Y to speed up the car in the animation, or press Select to make it run backwards.
To play battle Trax alone, select Battle Trax made and cars for both players. After the green light, wait about two seconds before hitting the gas. Any vehicle not activated by a controller will be driven by the CPU.