There's another shortcut in Dinodino Jungle, right when you see the bridges, instead of going up the main one, make a sharp right and go up a small one with boost pads. Sounds easy, but extremely easy to fall off, so not much use.
In bowser's castle, you can cut off the hairpin turn by running across the ledge at full speed without a boost, but you must be running at full speed and have sharp aim or you'll fall, and if you do land, you must turn immediately or you will fall off the
other side. Not too useful either.
On Rainbow Road, I like to cut the corners on the snake of death after the spiral of death right before the pipeline to heaven. Very fun to watch your kart almost fall off but get back on. Even funnier when I almost fall off but don't get back on (all though that did cost me a few races

)
The hardest part of Special Cup is the turns I think, not the AI, because I think the AI is actually easier. I can finally get the turns now without even letting go of the accelerator, but it's safer to do so rather than fall off.