One way you might be discovering new areas is literally dropping into them. Which makes sense, seeing as Toad can't jump at all. When it comes to ledges he can't climb, often the best option is dropping down into them instead. There are multiple levels where dropping down onto ledges and enemies will be the best way to progress - especially in the case of enemies, since Toad can defeat them by landing on their heads, but of course, can't jump.