Note: This glitch only works in the Japanese version.

Hop in the canoe in World 3 and then use a warp whistle. On the Warp Zone map, move to the left and Mario will go off the island! Unfortunately, once you've moved off the island you won't be able to get back on it. You're stuck unless you use another warp whistle, which will place you by the #8 pipe in the warp zone.