Secret warp from World 1-2 to World 2 Get the Cat Suit in World 1-1 and wear it throughout World 1-2. After reaching the underground area in World 1-2, you will reach a pipe with two path towards the exit (one lined with coins). Once you come out of the pipe, there will be three invisible "?" blocks along the wall. Use these blocks to reach the upper area with a Koopa Troopa. After killing it, climb over the wall right above the Koopa Troopa to reach the warp to World 2.
Secret warp from World 4-2 to World 5 After coming out of the underground area in World 4-2, there is a mystery box with a warp pipe nearby. Run along the wall to reach the top of waterfall, then jump across the poisonous water to see the red warp pipe to World 5.