For these additional mysteries we've written this new guide to the game map's secrets. Tighten your backpack, adjust your helmet's lamp and start humming the trademark song of the most adventurous Toad there is...
Captain Toad in World 1: Pipe-Rock Plateau (3 places)
In order to find Captain Toad from very early in your adventure you'll have to find one of the trickiest hidden exits in the whole game (as it can easily go unnoticed). We're talking about W1 - "Piranha Plants on Parade". This will open up a new road southwards, where a green warp pipe is waiting for you. The Captain will salute you and reward you from the other end, a purple pipe upon the skull-shaped rock on Deep Magma Bog (World 6).
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The second meeting with Captain Toad is still triggered from W1. Specifically, on the north side of the middle portion of its map, in that rocky, browny area. You can press A to enter a hidden warp pipe Northeast of Badge Challenge: Parachute Cap I. The Captain will share with you a privileged view of Fluff-Puff Peaks (World 2) when you exit the yellow pipe.
The third hideout can be reached from an area that at the same time is hidden in World 1, when you go south from the fork right before the first Palace. Enter the green pipe and, in the underground zone, push A towards the top right corner coming from "Angry Spikes and Sinkin' Pipes". When you exit the purple wrap pipe, the Captain will give you a tease of what World 6 has in the oven for you.
Captain Toad in World 4: Sunbaked Desert (2 places)
One of the peculiar mechanisms in this area are those three prominent paving stones with a lighting question mark acting as switches to open the stone gate right in the middle of the map. If you step on them, the passage will open and, after a Break Time and a course, you'll be able to reach the end and press A to enter a golden pipe to Shining Falls (World 3). There, Captain Toad is waiting for you at the other side of the golden falls.
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If you want to find the Captain Toad once again from W4, take the left path from "Secrets of Shova Mansion" and then circle around the block to press A. You'll exit from a green pipe surrounded by purple smokes, which means the Captain will treat you to an exclusive look at Fungi Mines (W5).
How to unlock the Special World in Super Mario Bros. Wonder
The most interesting thing about this bonus world is that, even if it is post-game content and something you don't need to beat to see the credits roll, you can start warping to it form each and every standard world in the Flower Kingdom, and thus it's possible that you've jumped in a different order, or that you haven't found the exit from a certain world yet.
Warp to the Special World from W1: Pipe-Rock Plateau
Access to Special World from World 1 is found at the peak of the plateau, in that rooftop-shaped, grass-covered formation that seems so obvious from the kingdom's overall map. To reach it, you first have to find "Bulrush Express" secret exit, which is pretty easy if you keep your Elephant suit towards the end of the level, to deal with the blatantly-placed brick wall.
Warp to the Special World from W2: Fluff-Puff Peaks
If you want to leap to the Special World from W2, you need to take the road heading east from the second open area in thee cloudy world, above "Pole Block Passage". Complete the level and the expert badge challenge to reach a higher cloud taking you to the bonus world in the sky.
Warp to the Special World from W3: Shining Falls
In the world of trials, the access to the Special World is not about putting your skills to the test, but your perseverance. To open up the path enter the Royal Seed Mansion once again. Master Poplin, who previously offered you a shortcut back to Petal Isles to the east, will now follow suit to the west.
Warp to the Special World from W4: Sunbaked Desert
Logically, this is where you'll find a greater number of mirages and illusions, both in the map as within courses, as it's a desert after all. Access to Special World from here is also quite interesting as, at the same time, it solves the mystery of the hidden exit from "Secrets of Shova Mansion". Or, in other words, how can I survive the Bowser statue they're pushing against me?
Keep calm and listen, it also happened to us, and it's just horrifying to die several times by being smashed against the wall. So stop trying to sneak under the statue with the Drill, or to wall-jump over it with badges, as it's just impossible. What you have to do, and the hint was given by the talking flower, is to push the right wall yourself!
From there, you can use the stairs and, after a course and an expert badge challenge, you'll reach the skies.
Warp to the Special World from W5: Fungi Mines
Similarly to World 3, it's not about finding a hidden exit, but about insisting. If you enter "Operation Poplin Rescue" a second time, the four buddies will thank your kind help by digging out an alternative path, this time to the west of the exit to Petal Isles.
Warp to the Special World from W6: Deep Magma Bog
If you see this map as a three-floor underground expedition, the access to the Special World is at the left end of the deepest and hottest basement. Meaning, if you complete the courses and challenges from "Wavy Ride through the Magma Tube", you'll end up landing on the platform to the skies.
Warp to the Special World from Central hub world: Petal Isles
When you've come full circle around Bowser in this hub world, after leaving the volcano, you'll return to the starting point where you came from W1, only that now you'll get a new shortcut to the Special World.