The Princess's Secret Slide

The Princess's Secret Slide is one of the first secret courses accessed in Super Mario 64 and Super Mario 64 DS. On Super Mario 64, it can be accessed by the right window from the room locked by a 1-Star Door on the top right of the foyer in Princess Peach's Castle. In Super Mario 64 DS, this room is larger to hold the locked doors that the other playable characters are in, along with there being two windows instead of three.

The secret course is home to two stars in total. The first star can be collected by going down the slide normally, and reaching to the ! block on the end of the slide to jump on to get the star. The second star can only be collected if the player reaches to the end of the slide under 21 seconds.

Notably, the Princess's Secret Slide is the only level in the entire game, including all the main courses, Bowser stages, and secret courses, to not feature a Red Coin star.

Secret Slide Dimensional Rift
The theory of The Princess's Secret Slide being a dimensional rift revolves around how it does not appear inside/outside of the castle itself, and how it is impossible for it to be accessed like this if it were to be taken onto a logical standpoint. Since it seems to be related towards the castle itself, it is possible that it doesn't have the same sort of mechanics to be accessed as the paintings the player takes to get to courses. Along with this, the place itself takes place in a black void skybox, meaning that it could take place in some sort of other dimension.

Other slides seen in Cool, Cool Mountain and Tall, Tall Mountain do not share this conundrum, as there are visible entrances and exits to the slides in the courses they are in.

Yellow Cap Switch
Looking through the files of the game, it seems that The Princess's Secret Slide was originally going to use the Yellow Cap Switch and an unused springboard object. This is shown because the secret course shares the same actor group as other cap switch courses (which is known as group8 in the decompliation). It is possible that this course was originally going to have used the Yellow Cap Switch for the course, using the Koopa Shell to slide through the level, since the Yellow Cap Switch was supposed to be used to unlocked boxed Koopa Shells.

Since this course is one of the first secret courses to be found in the game, it could be a possibility that the Yellow Cap Switch being the first one unlocked would be a reference to Super Mario World, as the first switch palace in that game would be of the Yellow Switch Cap.

Location Oddity
If the player gets their first Power Star in their game, the text used congratulating the player for it erroneously states that the location of room where the entrance The Princess's Secret Slide is would be in the second floor of Peach's Castle. In actuality, the location is considered to be a higher part of the first floor of the game. This could be a simple typo, or a leftover for the original placement of the secret course.

Sliding For Red Coins
According to some reports of phenomena in the Princess' Secret Slide, there is a star that can appear in the level, either replacing the timed star or appearing as a third star, requiring the player to collect 8 red coins for the star to appear at the end of the level, with some reporting that it appears on the top of the final room. The red coins can appear in both rooms in the level, as well as on the main slide.

Trivia

 * The music in the level is the same one used when the player races Koopa the Quick.
 * There are 80 coins total in the level; 50 normal coins, and 6 blue coins from the blue coin block at the start of the course (which equal up to 30 coins total). It is not possible to get any more through Cloning due to not having any entity that can cause it.