This stage looks like it was ripped directly from the classic Super Mario World 2: Yoshi's Island. It's the first time that we've gotten a stage inspired by the classic, as the others that were named "Yoshi's Island" were based on Yoshi's Story and Super Mario World 1. The graphical style is strikingly similar to the direction that the original went, and classic references of the game are found everywhere.
For one, you'll occasionally see Fly Guys pass over above you, and a Support Ghost will also arise from the depths on either sides. Those special flowers that you could collect in each level will sprout up in the background during the spring portion, and if you position the camera to the top right, you'll see the planet in which you fought Raphael Raven.
Fly Guys are basically an improved version of Shy Guys. The sole difference between the two is that Fly Guys can, well, fly, while normal Shy Guys can't. The only purpose that they play in Brawl is to indicate which season it is. If there is only one Fly Guy, then the season will correspondingly be spring. They can't attack but they can be attacked!
Support Ghosts could, as one might expect, be found in the Yoshi's Island series - specifically the haunted portions! They'd support Yoshi and Baby Mario somewhat if the duo flipped a pot with one in it over. Following this, the Support Ghost would raise the pot with the two of them on it and the duo could access higher grounds. It's not like the ghosts were trying to actually support Yoshi, so its name may not exactly be fitting.
Raphael Raven's Moon
Raphael Raven is a large raven like creature who was fought on a small moon. The mechanics of this fight changed slightly in that you could traverse the entire moon - meaning you could go under, above, and sideways (could this have influenced Super Mario Galaxy?). The tactic to this fight was to ground pound the peg on the moon when Raphael Raven is stationed on the exact opposite side of it so that it'd just back into the ground and then back the other side, thus harming the creature.
The Chain Chomps found here were found in an early stage of Yoshi's Island - when Yoshi and Baby Mario were peacefully minding their own business, Chomps would fall from the sky and crash through the ground, leaving a rather large hole. In the Mario series, they first appeared in Super Mario Bros. 3, where they were connected to chains. They would become a popular enemy throughout the entire video game series, appearing in multiple other games including but not limited to Super Mario 64, Super Mario Sunshine, and the recently released Super Mario Galaxy.
Goonies have only appeared in this series. In the series there were a variety of Goonies - ones that walked on the ground, ones that flied in the air, and finally skeletal Goonies that could, despite having no feathers, also fly in the air.
The Flowers featured in the background during the spring portion of the level were also found in both Yoshi's Island and Yoshi's Island DS. In the game, there were five in each level. In order to get 100%, you had to get each one. On occasions, there would be enemies disguised as these flowers and when you approached them, they would reveal their true form and charge you. However, these could be jumped on to get a boost and get higher up.