All Just a Dream: Doubly subverted! The instruction manual implies that Mario first dreams up Subcon, then sees it for real on a picnic with his friends. But the game's ending explicitly shows that he dreamed it all. But the game's sequel, BS Super Mario USA, implies that the events of the game did happen, and that Mario was actually within a dream world.
Canon Immigrant: Any monster or object from this game that shows up in another Mario game, considering they're all from DDP. Birdo, Bob-ombs, Pokeys and the Shy Guys? Not Mario characters... at least, not originally.
Snifits to a lesser extent.
Ninjis appear in the very last corridor of Super Mario World before Bowser, though they become an enemy you can simply stomp on to defeat. They are also seen in the first Paper Mario. While it's dubious as to how "canon" that series is, it's at least always pulling from the more accepted elements of Mario "canon".
Pansers, which resemble fire-spitting Piranha Plants, are the first of four Piranha Plant-like fire-spitting enemy seen in the Mario series, even if these particular enemies aren't seen again. (they're the most dangerous of the four, as some of them can walk.)
Cartoon Bomb: Mousers throw these and you can occasionally throw them too.
Competitive Balance: All of the characters have different jump strengths, pickup animation speeds, and running speed while holding an item (without holding an item, all of them run at the same speed).
Divergent Character Evolution: Luigi's higher jumping skills conveniently are also introduced here, but this game also gives him his characteristic flutter jump to go with them.
The Dog Bites Back: In the ending, after the Subcons are released, their immediate first action is to crowd-surf a bruised Wart off while the Heroes are being heralded and then (implied by the symbols to the right side of the screen shortly after he disappears off-screen) is given an off-screen No-Holds-Barred Beatdown.
Extended Gameplay: In the Advance version, after beating the game you can go through "Yoshi's Challenge", which challenges you to locate two Yoshi eggs in Subspace in each stage. The tough part is that you lose your collected eggs when you die.
Giant Mook: In the Advance remake, you can find giant Shy Guys and Ninjis. Picking one up will cause them to drop a heart, effectively turning them into infinite sources of Hit Points.
Grievous Harm with a Body: Throwing enemies at other enemies is the main method of attack, along with throwing vegetables (and keys, and bombs, and almost everything else you can get your hands on) at them.
Hearts Are Health: In the remakes. In the original game your hit points are Hexagons instead.
Hitbox Dissonance: The player characters have life energy, but in order to connect the game to the rest of the series, they shrink when they only have one hit point left. But this does not actually reduce the hitbox.
World 7-2 has the Hawkmouth gate attack you when you pick up the crystal ball. Three whacks with the Mushroom Blocks will neutralize it and allow you to proceed afterwards (but if you take too long, you'll have to repeat the battle).
Fryguy in World 4-3 splits up into smaller fireballs after you hit him a few times, which can catch first time players off guard after being used to bosses being defeated after a few hits.
Koosh Bomb: All the explosions look like this, with "BOMB" written in the center.
Life Meter: One of the earliest uses of one in a Mario game. The meter initially starts at 2 units, but it can be extended up to 4 (or 5 in the GBA port) units. The extended health doesn't carry over to the next level.
Mercy Invincibility: What happens every time you get hit, along with knockback. However, the invincibility frames still tick down as the screen scrolls vertically, which means it can run out during scrolling and you can get blindsided without anyway to recover.
Pint-Sized Powerhouse: Toad is a rather short guy, but he can pick up things with lightning speed, making him the strongest playable character. (But the worst jumper, unfortunately.)
Princesses Prefer Pink: The debut of Peach's pink dress in an actual game (she's always had a pink dress in official artwork).
Quicksand Sucks: Desert levels have two types; the first takes about 7-10 seconds to completely suck you in and is quite easy to jump out of, the second (sand waterfalls) takes half as long as the first and renders attempting to jump out a hopeless endeavor, though fortunately the first type is typically near it.
Mouser, who appears at the end of Worlds 1 and 3. In Doki Doki Panic, Mouser also appears as the boss of World 5, but was replaced in this instance by Clawgrip for Super Mario Bros. 2.
Triclyde is the boss of World 2 and World 6.
In the Game Boy Advance remake, Triclyde's second appearance was replaced with the second Mouser appearance, whose place was taken by the new boss Robirdo, leaving Mouser as the only recurring boss.
Recursive Import: This game would come back to Japan under the title "Super Mario USA".
Remake Difficulty Drop: The SNES version is a lot easier compared to the NES version due to the fact that you can save. The Game Boy Advance version is even easier due to the floating hearts, random large enemies that drop hearts when you throw them... as well as the fact that you can save. The levels themselves aren't any easier, though.
Rouge Angles of Satin: In the end credits, "Hoopster" is misspelled "Hoopstar", "Clawgrip" is spelled "Clawglip", and both "Birdo" and "Ostro" have their names switched around. All of these mistakes are fixed in the GBA remake.
Schmuck Bait: The Game Grumps illustrate a good example here: sure, you can get all those coins, but if you expect there to be bombs in any of that row of five plants, you're wrong.
Scoring Points: Not present until the GBA version, which added in a scoring system similar to that of other Mario games (in which beating several enemies with the same attack earns progressively more points).
She's a Man in Japan: The beginning of the bizarre saga of Birdo, though its appearance in this game is actually an aversion.