These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Funny Moments: Quite a few of the end-of-world cutscenes, but two stand out.
For Castle #4 (Ludwig's Castle), after Mario presses the plunger, the castle takes off like a rocket, and a confused Mario watches as it soars into the air and impacts in a nearby hillside - which wears a bandage for the rest of the game.
For Castle #5 (Roy's Castle), when Mario presses the plunger, the explosives don't go off, so he goes over to inspect them... and they blow up in his face.
If you have the cape, you can fly over most levels. The same goes for the blue Yoshi, which can fly after eating any Koopa. Even worse, if you have a cape and a blue Yoshi (or any Yoshi and a blue shell), you can fly for a very long time without even having to mash the button.
The brokenness of the Cape extends to slowing down Mario's midair descent even more than either of the flight oriented suits in Mario 3, making landings a cinch, and its spin attack kills most enemies and blocks most projectile attacks, making Mario near-impervious for any reasonably skilled player.
The blue Yoshi is broken to the point that, combined with the cape and a few timed jumps, it absolutely trivializes Tubular.
Unlike every following Mario game, you're allowed to keep any items that you have if you quit a previously-completed level by pushing Start and then Select. This makes it possible not only to get out of falling into a Bottomless Pit, but to go into a level, get yourself a Yoshi and then load up and extra lives and power-ups, then go back to the map and rinse and repeat. Most subsequent Mario games would redress this by reducing you back to small Mario and stripping you of anything earned in the level other than extra lives when you quit the level.
Luigi in the GBA version is FAR more broken than in any 2D Mario game. Combine the floatiness of his jumps from Super Mario Bros. 2, plus the tighter control and higher jumps in general of this game, and platforming is completely trivialized even without the cape.
The Wiggler glitch in Forest of Illusion 1 makes Scoring Points ridiculously easy in the SNES version. Although the points Cap is significantly lower, as there's 1 less digit allocated to the score display.
Super Mario Western by Hyadain, a lyrical remix of World 1's theme featuring decidedly Gonk and skeevy depictions of Bowser and Mario, is often used to depict love triangles - love quadrangles if one counts poor Luigi, who's depicted as being a relative Bishōnen.
Throughout the game, Mario performs various methods of destroying castles after defeating the resident Koopaling. This has led to the "Mario's Castle Calamity" meme, wherein Mario tries to demolish a Nigh Invulnerable castle with methods that always blow up in his face.
Some people like the wonderfully dramatic, musical sting of the keyhole exits. Also, the pronounced stomping sound of jumping on a Chargin' Chuck is so recognizable that it was brought back for their return in Super Mario 3D World.
The sound the springs and note blocks make. BREE-E-E-E-E-E!!
Nightmare Fuel: The autumn koopa sprites invoke this. The autumn theme altogether may even qualify, since everything is dying.
Mario's death animation, which features his eyes becoming red.
The koopalings who are defeated by falling into lava. They let out a screech of agony as they presumably burn to death.
In the SNES vs. Mega Drive/Genesis Console Wars, it was this game that received the full force of Sega's bile for being the direct competitor to the Sonic the Hedgehog series, and was constantly lambasted in all Sonic media (sometimes via Lawyer-Friendly Cameo) for being 'slow', 'boring', 'old-fashioned', 'childish', etc. etc.
It extended to some of the other systems as well. One commercial for the Turbo-Graphix 16 starts with "The passive type plays Nintendo" with Super Mario World shown (hilariously, the next part says "The aggressive type plays Sega" with a clip from Sonic the Hedgehog playing).
Sunken Ghost Ship, the final level before the Valley Of Bowser. The section with Boos randomly appearing out of nowhere is quite frustrating, even when you realize that if you stay in one place, they can't get you.
Tubular (level 2) is a notorious example. The entire stage is basically making it across a giant pit with the P-Balloon Power-Up, except you need to actually stop and hit certain blocks to find more balloons, or else you're not gonna make it in time. On top of that, thanks to this, you're basically a One-Hit-Point Wonder, and you have to make it through fairly difficult attack patterns to hit said blocks. (Unless you can pull off the P-Balloon glitch (holding left and right at the same time, which is easy for ROMs but damn near impossible for an SNES D-Pad), which makes the level easy as cake.)
Awesome (level 4) is no slouch, either. A run across a slippery ice world with kicker Koopas sending shells at you every step of the way, followed by a platforming sequence over equally slippy narrow platforms with Banzai Bills, infinite flying fish, and finally a jump boost off a flying Koopa to another slippery platform to jump a decent distance to the exit pipe.
Outrageous (level 7) is a course that definitely lives up to its name, as Mario must run a relentless gauntlet of Wigglers, Amazing Flying Hammer Brothers, Jumping Piranha Plants, Bullet Bill cannons, pipes that require springboards to jump over (said springboards needing to be carried across several screens), and various other hazards.
Vindicated by History: As mentioned under Snark Bait, this game was the target of bile due to its competition with Sonic the Hedgehog, and, while it was a big seller and well-liked, it was widely seen as just another Mario game. Nowadays, it's a contender for best game in the series and one of the best games of all time. The main reason why is that Super Mario World was the first Mario platformer to heavily incorporate alternate paths that lead to alternate levels, creating a great sense of nonlinearity and choice. It only took time to discover all of the secrets.
The flavor text that appears after Mario defeats a Koopaling was originally uniform and didn't even list the specific Koopaling by name. Their names being mentioned as well as implied character traits (Wendy apparently liking to sing, Ludwig doing symphonies, and Iggy being demented) were added in by the localizers.
Notably averted with the Koopalings' names. Super Mario World is the first game to give the Koopalings names in the Japanese version, and the names adopted were the same one as the ones the games English localization created. Even then, the player has to stick around to the end of the end credits just to find them.
"King Scoopa Koopa": What King Koopa could have done to the cavepeople, Luigi and Yoshi after they mutated into Chickadactyls (make them his mooks, turn them into food, eat them himself, etc.). Luigi also provides some when he tells Mario it's a good thing he doesn't like eggs.
In "The Night Before Cave Christmas", Oogtar opens Bully's present, a Bob-omb. Before it explodes, Koopa frantically tells it not to go off until Christmas morning. What was Koopa really planning to do to Bully with that present?
Hip's volcano in "A Little Learning". The Mario Bros. turn the pipes around but how much of Dome City or Dinosaur Land could the lava that already spewed out have destroyed?
During Koopa's flashback in in that same episode, there is a Wheel of Fortune puzzle that is three letters in length (DUH). One year after this episode aired, the actual show would begin using three-letter puzzles in the Bonus Round.
Idiot Plot: "Fire Sale", "Send in the Clown" and "Ghosts 'R' Us".
Memetic Mutation: The entirety of the "Mama Luigi" episode, particularly "That's Mama Luigi to you, Mario! *wheeze*" Other notable quotes include: "Well, it's like they say in Brooklyn: Early to bed, early to catch the worm. Or, is it the bagel?", "Mario, wherever you are, HHEEEEEEELLLLLLPPPPPP!!!", and "Luigi, King Koopa has the princess locked up in his Coney Island Disco Palace!"
From "The Yoshi Shuffle": "It's a stone, Luigi; you didn't make it!"
Suspiciously Similar Song: Once again, each episode contains a musical montage. Except this time, they used this from the start rather than using a cover song. For example, "Ghosts R' Us" uses a knockoff of Thriller, "Born to Ride" uses one of Born to be Wild, etc.