Checkpoint Glitches
Luigi Raceway
This one only works on the Japanese versions because the section does not have hit detection in the other releases (you fall through into the tunnel). By crossing over one of the polygon seams shown by the arrows in the picture, you change the path location of the highlighted blue section. You will then get placed behind the finish line at the end of the lap by jumping out of bounds in that section.
Royal Raceway
By crossing over the polygon seam shown in the picture (jumping from path -38 to -44), the path location of the top of the stands will change allowing for a lap skip by jumping off them from the back and into the water while crossing the finish line mid-air. The checkpoint gets reverted if you touch the grass directly in front of the stands or jump back off of the stands anywhere except into the water.
The new lapskip variation found by Forest64 requires driving over an earlier polygon seam in the grass and specifically not hitting the one pictured above. Need to create a new image