In the Nyakuza Metro DLC, there is a hidden area that can be accessed in the Green Clean Station by jumping off of a moving subway train at the last second and then wall-jumping up to the top of a large, green, three-tiered LCD display above the station ledge. At the top, a cage with an egg can be found, but just near it is a Springboard that will send Hat Kid to a hidden grated area through a manhole. Upon interacting with the manhole, a message can be found on it that reads "Kiwami means extreme.". Suddenly, an eye-patched Metro Cat named Meowjima will ambush you by jumping out of the manhole and screaming:

"HAT KID-CHAAAAAAN! You've grown soft, time to bring out your fighting spirit!"

before initiating a secret mini-boss battle. The message on the manhole is a reference to the tagline of the game Yakuza: Kiwami, and this character is a parody of Goro Majima based on his appearance in that game as well as a reference to one of its side quests "Majima Everywhere", where he ambushes Kazuma Kiryu through disguised encounters as a form of training.
Contributed by MehDeletingLater
In Hat Kid's spaceship, waiting 20 minutes will cause the music to go silent, before a loud, inexplicable groaning noise plays in the bedroom.
Contributed by game4brains
Jonas Kaerlev was concerned about bringing the game to Kickstarter, because he thought people would associate it with Donkey Kong 64, rather than other titles of the genre.

"It did worry us before we launched the Kickstarter. But we thought if we emphasized enough that we were trying to make something less like Donkey Kong 64 and more like Banjo-Kazooie or Mario 64, we thought it would be much more well-received."

Jonas also stated the lack of collect-a-thon platformers was partially because of Rare's Donkey Kong 64 game.

"I don't want to blame it all on Donkey Kong 64, but it's partially at fault. Donkey Kong 64 did a lot of things wrong, in that it was very tedious to collect everything in order to move on. A lot of people don't want that. They want to be able to breeze through the game if they so desire, but there are also people who want to collect everything, and get stronger and better."
Contributed by CLXcool
In the Beta version of the game, there was a milkman NPC that was a Mafia member in a milkman suit. For some reason, the Milkman was not present in the final release of the game.
Contributed by Smirkytrick
In Act 4: Train Rush of Chapter 2: Battle Of The Birds, a T.V references the intro to Kirby's Adventure.
Contributed by jjbones123
In Queen Vanessa's Manor, there is an entire third floor that went unused in the final build of the game, along with what appears to be a shadow version of Hat Girl. The reason why the floor was cut was simply because the developers didn't like how it turned out. It is still in the game, but it cannot be accessed through normal play.
Contributed by Smirkytrick
Jon Jafari aka JonTron, who voiced the Jazzy Penguin in the game's prototype, was originally asked to voice a different character. The developers thought his voice didn't match the proposed character, and instead made him the voice of the Jazzy Penguin. Jon would later end up voicing the secretary of Dead Bird Studios instead in the final game.
Contributed by KnowledgeBase