The Super FX chip (for SNES games like Star Fox) got all the hype, but SMB3 was actually the first first-party game to have extra hardware built into the cartridge. They added a chip that enabled split-screen scrolling, which is how the game could display the full-width, stylized "status panel" at the bottom of the screen with your inventory, score, lives, timer, etc. while still showing the fluid full-screen scrolling game world.
They also used every last scrap of system memory they could get; ever notice a handful of "glitchy" pixels on the left side of one row right beneath the gameplay before the status panel? It's visible any time you're in a level (not the world maps or bonus games) and it's constantly updating and changing:
That's an extra bit of display buffer memory they're using as scratch space. Those scanlines were never used during gameplay (they were part of a little border between the gameplay portion and the status panel), so they figured they could get some extra bytes of memory to play with at the "cost" of having a little glitch where people weren't likely to notice. Cool stuff!