Play tournament mode and complete the first three championships (Mushroom Cup, Flower Cup, Star Cup) to view the credits, and watch some animated outtakes from the opening FMV sequence. Successfully complete the next three championships you unlock from this (Rainbow Cup, Moonlight Cup, Planet Cup) to view the credits again, but with entirely new outtakes.
At Mario Tennis title screen hold Z button while pressing start to unlock Event mode. This is a tiebreak game, you are able to select from 3,5, or 7 points. This does not remain unlocked however, you must do the code every time.
To get a character's star version, just beat the 3 tournaments of the Normal Cup with a character and you will get the star for this character.