Each time the spinners start in the bonus round, the second symbol in the first slot is always a cherry. Do it correctly, and you can guarantee yourself an average at least one extra life per coin.
Fast ending
On world 4-1, get the princess. Go up the vine, but go left, run, and fly to a secret door. Go through the door and use the bombs to blow up the wall. Then, jump over the top of the screen and run left.
Finding Fry Guy
Use the Princess in world 4-3. A castle will appear after crossing the lake. Do not enter the castle. Instead, fly further across the lake to find another part of the castle. Go through the second door to fight Fry Guy.
Maximize your coins
When you use the magic potion to get the mushrooms, do not pick up the surrounding vegetables (which are coins in the magic door) immediately. Find the location in each level where there are the most vegetables that are close together. Drop the magic potion and go in the door. Pick up as many coins as possible. Repeat this once, after doing something that will make the potion reappear (such as climbing a vine, going down a pipe, or entering a door).
In world 3-1, take Toad (because of his lifting power). Fall down the waterfall onto the platform where the door is at the bottom. Enter the door and get the magic potion. Drop it anywhere there is a continuous stream of coins. Enter this door, and grab as many coins as possible. Go out the door you came in, then return, and repeat once.