I explain the usefulness of pause buffering. There are two primary purposes: to pause buffer inputs and to pause buffer the global timer.

Pause Buffering Inputs: Normally, if we input a button (such as A or B) on two consecutive ingame frames, then it won't count as two presses. Instead, it will only count as one press, held for two frames. However, if we use pausing to separate those two ingame frames, then it is possible to press the same button on two consecutive ingame frames.

Pause Buffering the Global Timer: The global timer is a variable that starts at 0 when the game is turned on and increments once on every frame, including paused frames. Some phenomena in the game rely on the global timer, and expect it to increment normally. However, by pausing strategically, we can control exactly what values the global timer has during the ingame frames. This can lead to some rather strange things happening.

Thanks to Peter Fedak for telling me the specific details of how the snufit and swooper variables are calculated:
(1) snufitHeight = 8 * cos(4000 * globalTimer) + startingHeight
(2) swooperRoll = swooperRoll + 1000 * cos(20000 * globalTimer)
(3) swooperYaw = 1200 towards 3000 * cos(4000 * globalTimer) + targetYaw
Note that concerning (2), Peter said that the roll also takes a step of 500 towards another number he hasn't yet determined.

Additional Notes
(1) Objects in 3D space have 3 angles: yaw, pitch, and roll. Here's a diagram for reference: http://i.imgur.com/E05roYE.png.
(2) There are some other events in the game that utilize the global timer that I missed in this video, which can be found here:    • More Global Timer Dependent Phenomena