Model Dissonance: Notably saved memory by making clouds and bushes the same object, but rendered different colours.
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.
Riddle for the Ages: Nobody knows exactly when Super Mario Bros. was first released in the United States. Nintendo of America gives a date of October 18, 1985 as the "official" U.S. release date (as reflected by Super Smash Bros. Brawl, the Virtual Console and other places), but several sources disagree with this date, with some claiming the game wasn't released until the national launch of the NES in 1986. A couple of attempts have been made to clarify this situation, with limited success.
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.
Spinys weren't 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.
The multi-coin blocks were initially intended to be single-coin blocks, but a glitch resulted in them giving multiple coins. The bug was fixed at one point in development, but was later brought back as an actual feature because they were so popular with the programmers.
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).