Move Luigi next to an enemy and jump, then press jump again at the peak of Luigi's leap. If your timing was right he'll jump even higher.
Get a magic potion. Hold it until a star shows up. Grab the star and put the potion down while you're still invincible. Enter the door you just made and wait. Just before your invincibility wears off, exit the door and you'll hear the original Super Mario Brothers theme song.
Pick up a vegetable then find an enemy, preferably one in the air near the height of your character. Get directly next to him, wait for him to get to the top of his jump, throw it, then immediately run after it. You should end up catching it. Also,you can sometimes get on top of thrown vegetables after hitting an enemy or two with them and pick them up.
World 5-3 Climb up ladder to begin level. Pull up first plant from ground, it is a shell. Release shell then jump on. The shell will continue to go back and forth killing the bombs thrown by the albatrosses. After 6 or so the knocked off bombs turn into 1-up's. Sometimes the bombs are dropped on you or close to you. It does help to duck down to avoid these. This works on Game Boy, I'm not sure about other games.
In level 1-3 go to the area just before the brick background. Pick up the plants until you get a bottle. Then go past the brick background until you find a pot and throw the bottle on it. Go through the door and down the pot into World 4.
To warp to level 5, first get to level 3-1. When you enter the first door, fall all the way down. You also have to be in the middle as you fall. When you stop, you will find a platform with a door. Enter the door, then you have to look for the potion in the grass. Pick it up, then throw it on the ground, enter the door in cyberspace, and go into the vase and you will be at level 5.
In level 4-2 In the area with the whales find a bottle and throw it on the next pot. Enter the doorway and go down the pot into World 6.
Work your way to level 5-3. (It would be a good idea to choose Luigi for this level because of his superb jumping skills.) Go up the ladder at the beginning of the level, and then jump up onto the ledge above the ladder. As soon as you get on top of the ledge, grab the first grass on the right. It is a potion. Use the potion and go through the door. Now, while in Sub-space, go down through the jar and voila! Now you're in Level 7!