World 2, like many of its counterparts in the Mario franchise, takes place in the desert. However, it features a variety of terrain, such as flat plains for facing Lakitu, a wide oasis and a completely airborne platform ride. There are more red Toad Houses than green Toad Houses, and all but one requires Star Coins to obtain. This is one of two worlds that can lead to two other worlds. Depending on how one defeats the world boss, the following world would either be World 3 or World 4.
Back at the room that can be flooded, there is an opening in the ceiling. When the room is flooded, you can swim into the opening to reach another chamber with a bunch of coins you can collect. However, if you swim up fast enough, you can also see another switch, this time hanging from the ceiling. The switch is only visible when the first switch is still active, and pressing it will flood the room even further. This will let you swim up more to reach a hallway at the top. Exit the hallway to reach the red flagpole.
This alternate exit opens a path to World 2-A, which itself leads to some major shortcuts.
Above the green Warp Pipe that takes you out of the oasis is an alcove with the yellow Warp Pipe. After you jump up from the last Spin Block, drift right and attempt to land on the red Koopa Paratroopa, which will bounce you up to the yellow pipe. Go through it to reach a blocked-off section of the original flagpole area, where you can obtain the third Star Coin. Go down the red pipe to be taken to the red flagpole. Jump to the right of the two blocks to hit two more hidden blocks, which will help you jump to the top of the flagpole.
The secret exit leads to the World 2 Cannon instead. This cannon sends you to World 5. The extreme change in climate isn't the only big difference between the two worlds, and the increase in difficulty can be hard to overcome.
This exit requires you to be Mini Mario to reach, so the hassle might not be as worthwhile as the secret exit in World 2-3, since the shortcut you unlock isn't as far. If you happen to have a Mini Mushroom in reserve or want total completion of the game, descend to the underground lake. As Mini Mario, you can walk on the water and pass through a gap at the left edge of the lake. This will take you to a mini Warp Pipe that leads to the secret red flagpole.
The secret exit opens a long path around the main route of the world that lets you skip past a few levels straight to World 2-6. You will also unlock a red Toad House on the way.
Defeat Mummipokey as Mini Mario. Due to the reduced power of Mini Mario's jump, you need to use Ground Pounds instead to damage it. If you have a Mini Mushroom in reserve, you can enter the fight normally and damage Mummipokey a few times before using your Mini Mushroom and dealing the final hit. As long as you finish off Mummipokey while in mini form, you have succeeded.
Defeating Mummipokey unlocks World 4.