After beating the game, press any button while you're on the title screen. The cursor will change from a mushroom to Mario's face. Press to play a new Expert Mode that features enemies which are tougher, more numerous, and in different places.
If you manage to beat Super Mario Land in Expert Mode, return to the title screen, and press . Doing so activates the Stage Select. Every time you press A, you advance the stage you start on by one level, until you wrap around from 4-3 to 1-1.