Super Mario... (wait for it)...
The working logo for the game was very simplistic, only reading "Super Mario" and having a Bob-omb by the side of it.
Super Mario Can't-decide-on-a-logo Galaxy
Another logo was used a lot during development, until it was replaced again by a much better logo.
Sūpā Mario Can't decide on the final logo
Not even Japan was safe from the logo changes. Originally, the logo had the japanese name of the game at the top and the original game name as a subtitle. This was swapped for the final release.
Now you see me, now you don't.
In the game's code, another playable character can be found. By making it appear on the screen select menu, it appears to be named Oh fiddlesticks, what now? (A reference to Portal 2's "sound missing" sound which is a quote from Dr. Kleiner from Half-Life 2) although in the game's code it's referenced as Toad1.
In the character select screen, it uses the default character placeholder image (Which coincidentally happens to be a Toad silhouette with "PLACEHOLDER" on it), and selecting it lets you play as a very glitched up Toad NPC. In this mode getting hurt, jumping or falling crashes the game because of missing animations and grabbing a powerup softlocks the game for unknown reasons.
Super Mario 3D Galaxy... Maker?
One of the entries in the game's code is for Builder3DS. Activating it allows you to enter a menu where it will ask you to put a game called Super Mario 3D Galaxy Maker on a 3DS and connect it to the console. The logo for the game uses the second logo with "Maker" at it's side.
Obviously, this game doesn't exist, but some gameplay screenshots are shown in the menu.
The concept of the game was that you could make your own levels like in Super Mario Maker, but you'd have to play them on your console in Super Mario 3D Galaxy. It was most likely a free game.
Originally, the Technocolor Mushroom had a very ugly and unprofessional appearance. It was a mushroom with different colored mushrooms around it. It was replaced with a more polished design.
Sometime after the change, the design below was changed to an animated look.
There are several files in the game which are variants of "GameLine". All of them are .nfo files that, when opened in a text editing software, show an ASCII of the first logo (the one that read "Super Mario").
Leftovers... from other games?
Strangely, there are at least two pieces of unused content that doesn't belong to Super Mario 3D Galaxy. One of them is the following text from UNDERTALE that also goes ununsed in that game:
"Somewhere^1, a quiche's worst& fear becomes reality./%%
A quiche in another timeline./%%"
The next one is the unused Gold Cheep-Cheep from Super Mario Bros. 3:
The Quest for the Grand Star
Aside from the character placeholder (A Toad silhouette with "PLACEHOLDER" on it), there are more placeholders. While most are just black boxes with "PLACEHOLDER" on them, there are some which are actually miscellaneous images from The Quest for the Crystal of Plot Importance, a game made for a contest.