I notice that the CP players can fall through soft platforms (i.e. those that you can fall through by pressing down while standing on them, such as in Dreamland) as they are coming down from being airborn. Is there any way that a player can pass through a platform as they are falling down without first landing on the platform?
After you finish an up B move and enter the "helpless" falling state, you can fall through soft platforms by simply holding down on the joystick. This state is the only time you can fall through a platform as if it were not there.
Not all characters can do this. Examples include Kirby (the final down-stroke of his final cutter up B does not ever finish until interrupted by landing/getting hit/blast zone) as well as both Jigglypuff and Yoshi (the two non-jumping up B's). Also Falcon's up B does not make him helpless if it connects with an opponent (but does remove his second (aerial) jump). A related special case is Fox's up B (the fire fox) can also pass through soft platforms during the move itself, when aimed downwards.
In all other cases, you can't fall through a platform per se, so it must be done in two steps: land, then drop through. Given enough practice with the timing, it is possible to perform the two step sequence fluidly and almost seamlessly. The fastest way to drop through a platform from a standing state is to "shield drop" by pressing Z and down on the stick at the same time. It saves a frame or two of ducking animation compared to the normal smash the stick downwards method, and also works while running/dashing.
It's all in the timing, you have to double tap down as you're about to hit the platform and you'll land on the platform below.
I'm not 100% sure, it's been a while since I played an N64, but if you are on a platform and pass through it and if you hold down you will just continue through lower soft platforms.