Raccoon Mario can fly, but real raccoons can't. Additionally, he gets this power from a leaf. What do leaves have to do with raccoons?
The same reason turtles can breath fire, mushrooms can make you grow twice as tall, walking mushrooms can fly, and you can get to dungeons through giant green pipes.
Actually, it's not a raccoon; it's a tanuki, which in Japanese folklore use leaves as part of their magic which adds more confusion with the Tanuki Suit as it's literally just a slightly more amped up Leaf powerup but with the added advantage of being a priest statue. Along with the Frog suit, SMB 3 is pretty steeped in Shinto themes.
At first it isn't clear why the king of World 3 looks like Mario. On closer inspection, his castle is in an island chain vaguely shaped like Japan, and his castle corresponds to where Kyoto (and thus Nintendo's headquarters) is in real-life Japan.
Furthermore in the original game the king was turned into a Kappa, a Japanese folk creature and the inspiration for the koopas.
Certain levels in the last world don't make sense to you? Well, the tank and ship level are obviously Bowser's Army and Navy, respectively. The levels with the hand that pulls you under are prisons. The final airship level with the tiny platforms? That's Bowser's Air Force. The last tank level where you are being fired on from above and below? That's the last of Bowser's tanks and airships moving in together for a final assault with the airships moving to almost ground level to attack.
In Super Mario Bros. 3, the main plot has you traveling from world to world, defeating the Koopalings, and stealing back the wands they stole from various kings who have been the subject of a Baleful Polymorph. After the 7th such world, you learn that the Princess has been kidnapped and rush to her rescue. But what if you used the Warp Whistles to skip ahead? Are the kings of the worlds you skipped trapped in their other forms? Do those Koopalings retain their wands and continue to cause havoc?
And then there's the Plot Hole of what happens when you're in World 6 and you can actually use a whistle to go back to World 5. Even if you've completed World 5 already, the story has rewound to the beginning of World 5, as if you'd never completed it and never retrieved the wand.
Speaking of the wands, in New Super Mario Bros Wii',' the Koopalings have the exact same wands they had in Super Mario Bros 3''. Since the seven Mushroom Lands and their kings have never been mentioned again, it's quite possible that the Koopalings went back to the Lands and got the wands again... and left no survivors...
This one is highly subjective, of course, but Bowser has eight kids, the seven Koopalings and Bowser Jr. (not to mention the possibility of the Koopa Kids). Bowser is never seen with a wife of any sort, and he constantly tries to kidnap princesses for no apparent reason. Think about that for a while. The whole "Mama Peach" thing from Super Mario Sunshine doesn't help much either. Although at the end of the game, Bowser admits that Peach isn't really Bowser Jr.'s mother.
Arguably, this is still Fridge Horror, since the fact that Peach had to think about whether or not she a) had sex with a giant fire breathing turtle and b) given birth to said turtle's son, also a giant fire breathing turtle, and came to the conclusion it was true means that she must be the mother of at least one of Bowser's kids.
Perhaps she's just not that bright and doesn't understand how having children works?
Or the idea is so absurd that she needed time to process it in her mind.
Remember Yoshi's Island? Babies in the Mario universe seem to be quite literally delivered by storks. It's possible these people have no idea how actual childbirth works.
Bob-ombs. When they were first introduced, they were merely mindless robotic automatons that would explode after a certain amount of time. Not so bad, right? But, now, in the later games, the Bob-ombs are now sentient and they still explode after a while. Yes, folks, we now have a game series that features suicide bombers.
And, it turns out that there's also a war going on between the good pink-colored Bob-ombs and the evil black-colored Bob-ombs. So, now you have intelligent bombs who are not only willing to blow themselves up to kill Mario, but also are willing to blow each other up as well.
If it helps, in Paper Mario, you learn that Bob-ombs get better from exploding a few seconds after the fact, and will do so willingly to clear debris or just blow off steam.
Speaking of sentient weaponry, there's Bullet Bill, Banzai Bill, and Torpedo Ted. Sure, nothing seems too terribly wrong as they're just large bullets/torpedoes zooming across the screen. But, then you notice that they have a face and (sometimes) arms. So, are they either all just designed that way to simply look more intimidating, or are they alive?
One of the levels in World 8 has a substance that seems to be lava, but Mario can swim in it. It moves like water on the world map. Off-color water? It's blood.
Or, y'know, muddy water.
When you kill all the suns in Super Mario 3. what ramifications does that mean for the Mushroom Kingdom or whatever planet Mario lives on?
Not much considering those 'suns' are only slightly bigger than Mario himself. They're just normal enemies.