Are there any mechanical differences between the nine levels of CPUs besides their AI? That is, are harder CPU players given bonuses to their speed, damage, etc? For example, many strategy games give more difficult computer players advantages like omniscience of the board, bonus resources, etc.
Higher CPU levels don't give any speed bonuses, heavier weight, stronger attacks, or anything. They also don't change the actual AI of the character; each character has an individual AI that is the same regardless of their difficulty (in addition to some common AI routines).
The only difference between the different levels is that, at higher levels, a CPU is more likely to do something. Take perfect shielding as an example: all CPU levels can do it, and all of them come to the conclusion that they should under the same conditions, but the chance of them actually doing it instead of standing there and taking the hit is rock-bottom for low CPU levels and super-big for higher ones. (AI-hacking topics like this one make zero mention of CPU levels and are generally written as if they're assuming that levels are not a factor.)
I also found this image of what the common AI is as extracted by one of the best in the field:
As you can see it makes no mention of CPU level.
According to the Smash Bros Wikia,
So, there's a (good) chance that the AI has impossibly-fast reaction speed. However, the AI does not get any extra damage/movement speed unless you give it a handicap.