I've managed to bypass two worlds, and don't know how to get into them. Little help?
Hint: Remember when you beat the bosses of the worlds beforehand? If you don't know what I'm talking about, go beat them again. And if you just want to know...
You need to beat the bosses of worlds 2 and 5 as Mini-Mario. Then you'll go through the tiny passageway rather than the default one.
For ways other than the one I hinted at, you can find the right cannon to launch yourself to the extra worlds.