Super Mario Bros. 3 is the first Platform Game to be able to scroll in every direction, including diagonally. Previous Platform Games were limited to straight up-and-down or straight left-to-right.
Author Phobia: Chain Chomps came from an experience Shigeru Miyamoto had as a child, when a dog chased after him as he approached but stopped just inches from him because the dog was tied to a stake.
What Could Have Been: The dolphins that ended up in Super Mario World were originally planned for this game, but never implemented for whatever reason. This probably explains the abundance of "rising water" levels as well.