After you played for a while, you'd see that CPUs generally run in the same route on a track. You could then place a banana peel/green shell at that spot, and you would hit someone every time.
CPUs only used their character specific items. Mario's and Luigi's star power didn't even make them go faster. No CPU had access to lightning bolts.
You're right, CPUs did ignore things like character stats such as acceleration, but they didn't always keep up with you. On a lot of tracks, you could get a pretty big lead and keep it. While SNES MK did have some rubber-banding, it's no where near as harsh as it is currently
But anyway, has anyone played much online? Nintendo did such a good job. I also loved how I got a friend request on the Wii message board. Not having to input a code to add my friend? Awesome!