Also, when converting a game to a new platform (whether by porting or emulation) it's often helpful and sometimes necessary to consult the original development team and documentation (like the source code), which Nintendo probably doesn't have access to since Rare left for Microsoft.
Throw It In: The DK Rap was originally written as a joke by Grant Kirkhope, but the developers liked it enough to include in the game.
Urban Legend of Zelda: Several, the most notable being an inaccessible room in Creepy Castle with a glass wall. If you stand on the hallway outside of it and use a first-person perspective, you can see a tall, carved stone pillar with a Monkeyport (teleportation) pad for Tiny nearby as well as a purple banana balloon floating over it. The room appears to be useless. King K. Rool's control room also features five steel kegs with the Kongs' faces painted on them. Probably nothing more than a little detail, but it sparked some speculation back in the day.
Until people learned how to get to the room. The Monkey Port pad is in the Stock Car Race room across the hall, behind the Frantic Factory model. In order to get into that room, you need to get Tiny into the ballroom. All Tiny has to do to get in there is have Diddy open the door and switch characters before it closes.
Fungi Forest was going to appear in Banjo-Kazooie as Fungus Forest, but the level was (among other levels) scrapped from that game due to time constraints. A picture of Fungus Forest can nevertheless be seen in Banjo's house.