Hydrocity's background graphics have swapped Acts, with Act 1 using Act 2's graphics, and Act 2 using Act 1's graphics. Although a majority of Mania's Act 2 is a 1:1 recreation of the original Act 2 of Sonic 3 & Knuckles' Hydrocity, the swapped graphics are mainly to foreshadow both Acts' bosses have switched, too. The second half of the new Act 1's boss brings back the original Act 2 machine to use against Eggman, himself. Meanwhile, the second half of the new Act 2's boss brings back the original Act 1's boss, this time being piloted by Eggman rather than being its own sentient machine. The background swaps also indicate a reversal of the "Act 1 mostly revisits elements from the source Zone while Act 2 introduces new gimmicks" pattern seen in most other returning Zones, as Act 1 features new elements such as rideable bubbles and boats, which are completely absent in Act 2.
The above point implies that Sonic and co. are actually traveling backwards through Hydrocity compared to S3K that is to say, they're entering at the Marble Garden end and exiting at the Angel Island end which in turn is also supported by another detail. The Zone immediately following Hydrocity is Mirage Saloon, which starts out with Sonic and co. riding the Tornado. The last time we saw the Tornado was during the opening cutscene and where did that take place, again?
Building onto that, the Zone that takes place before Hydrocity in this game is Stardust Speedway. Stardust Speedway was the second-to-last round in Sonic CD, coming right before Metallic Madness; Metallic Madness in Sonic Mania is the second-to-last Zone, directly preceding Titanic Monarch. This creates an interesting story detail where, after Eggman uses the Phantom Ruby to get Sonic and company out of his (nonexistent) hair at Press Garden, he soon realizes that he's just put Sonic within a few minutes' jogging distance of his HQ and the superweapon he's building, so he races over there to Phantom Ruby Sonic as far away from his HQ as he possibly can namely, near where he picked up the Phantom Ruby, i.e. Angel Island. Pity that he forgot about Sonic leaving the Tornado there...
The number of reimagined levels in Sonic Mania is based on the game they made their debut in. For instance, there is one stage* Green Hill Zone from Sonic the Hedgehog, two stages* Chemical Plant Zone & Oil Ocean Zone for Sonic 2 and Stardust Speedway Zone & Metallic Madness Zone for Sonic CD from Sonic the Hedgehog 2 and Sonic the Hedgehog CD, which can be considered and was developed as a sequel to Sonic 1, and three stages* Flying Battery Zone, Hydrocity Zone, & Lava Reef Zone from Sonic 3 & Knuckles.
If the new stages* Studiopolis Zone, Press Garden Zone, Mirage Saloon Zone, & Titanic Monarch Zone represent Mania itself, it's fitting that there are four of them, as Mania is a successor to 3 & Knuckles.
Stardust Speedway Zone uses Sonic CD time travel to take you from Act 1 to Act 2, with Act 1 being in the past, but Metallic Madness Zone, the second of two Sonic CD Zones used in the game, doesn't and is set in the present. Why? Because the Phantom Ruby doesn't drop you into that zone.
Tails no longer has his Flicky companions in his Super form. Why is this the case? The Flickies only appeared when Tails used the Super Emeralds in 3 & Knuckles. In Mania, Tails transforms with the less powerful Chaos Emeralds, so it's only natural he would be missing an ability.
The end of Mirage Saloon Act 1 for Sonic/Tails features Fang, Bean, or Bark attack the Tornado while the "Hard-Boiled Heavies Mischief" theme plays. This might at first seem to be just because it's a fitting theme to use, but once you find out that Heavy Magician is impersonating them, it becomes even more apt.
The Act 1 boss of Mirage Saloon is a recreation of a boss from Sonic Chaos. Sonic Chaos is the predecessor to the game where Fang debuts in,Sonic Triple Trouble. You fight Fang* as an illusion in Mirage Saloon Act 2.
Act 2 of Mirage Saloon is covered with wanted posters featuring Fang, Bean, and Bark. It's unlikely for them (well, Bark at least) to have committed any crimes that warrant a warrant, so why are they wanted? The boss battle brings about a likely answer: They didn't do anything. Heavy Magician committed crimes while disguised as them, in order to frame them and get away scot-free.
Which brings about another question: why did Heavy Magician frame them when framing Sonic and co. would've given our heroes more trouble? That answer, too, comes about with a little pondering: Fang and co. were better scapegoats. They've mostly stayed out of the public eye over the past several years, so they'd be unlikely to have publicly confirmable alibis, and they're not exactly model citizens, so they'd be plausible suspects.
Heavy Magician's ability to transform into Fang, Bean, and Bark makes a lot more sense after it's revealed in Sonic Forces that the Phantom Ruby which empowered the Hard-Boiled Heavies and Infinite is capable of creating illusions so realistic that Your Mind Makes It Real, and also can create constructs of characters complete with their respective abilities.
Super Sonic's and Knuckles' idle animations are an inversion of the infamous lyrics from Knuckles' theme song. Knuckles chuckles, Super Sonic flexes his muscles.
Ray is much more maneuverable in gliding than fellow glider Knuckles. Well, of course he is. Echidnas are ground-based species. Whichever way Knuckles learned how to glide, its not an innate ability. Ray, on the other hand, has gliding as a natural aspect of being a flying squirrel. In his case, its instinctual, so of course hes more proficient.
Intentional or not, Mania's seeming success in creating an alternative to Sonic 4 also includes an explanation as to why Metal Sonic would potentially go rogue in Sonic Heroes. Metal Sonic in Adventures is shown to be able to comprehend the emotions of his enemies enough to manipulate them via impromptu hostage situation, implying he's definitely getting smarter as time goes on. Between experiencing the power of the Phantom Ruby, being upgraded to be given a Super Form and Mecha Sonic's ability to siphon power from the Master Emerald, he would probably start seeking out power on his own. Not only that, while Eggman's plan in Adventures and Mania proper failed, the one plan he created on his own with no outside assistance succeeded. It's probable that he'd start to see Eggman as the key flaw in the Empire's operation.
Overlapping with Fridge Horror, in Encore Mode, Metallic Madness and Act 2 of Stardust Speedway use a palette inspired by their respective Bad Future. Why? Because you collected the Chaos Emeralds, not the Time Stones.
It seems odd at first that Sonic and Co. are completely confused when playing Puyo Puy- I mean, Mean Bean Machine. Wouldn't they remember the events of the game? Until you realize that A. The game itself took place in another continuity, and B. It's specifically pointed out in that game that Sonic and Co. was nowhere to be seen during Dr. Robotnik's Mean Bean Machine. Of course they won't remember how to play a game they never starred in!