Killer App: Really, the importance of this game can be easy to underestimate by today's standards. There simply weren't games like it. "Golden Age" games were more simple, and had fallen out of favor in the US due to the The Great Video Game Crash of 1983, and games on PCs were more complex, which meant they didn't have the accessibility or mass appeal. Some might dismiss its sales due to being bundled, but it was sold separately in Japan,note and in North America at first and was still a smash hit. This game helped sell the NES to a game-weary audience, and elevated Nintendo to the top of the gaming companies.
Saved for the Sequel: Miyamoto first planned for the game to be divided between "ground" and "sky" stages. In the sky stages, Mario would fly in a vehicle (at first a rocket, and then a cloud) while shooting at enemies with the beam gun. Those concepts never made it into Bros., but vehicular shooting stages in the sky (and sea) were later included in Super Mario Land.
Throw It In: Spinies aren't actually originally intended to fall straight down, and there's code in the game that can be patched on that will make them be thrown using an algorithm and bounce off blocks, similar to later games in the series. Due to a bug said code wasn't working, but it seems like nobody had a problem with that and decided to leave it as is.
At one point, Nintendo of America was planning to release the game under the title Mario's Adventure, as evidenced by this early flyer for the arcade version. Who knows why they considered changing the title, or why they ultimately decided not to.
This game was originally slated to be remade, presumably using the All-Stars graphics and sound effects, as part of the first Super Mario Advance game for the Game Boy Advance. The game was swapped out in favor of the American Super Mario Bros. 2 after Nintendo realized that they'd essentially given this game a handheld remake via Super Mario Bros. Deluxe (which coincidentally served as the inspiration for the Advance series).