Hmm. This looks like fun. Might as well throw in my opinions on the matter.
Out of the primates, these are my only 'problems'. Considering the hairless state of Meditite, Medicham, Machop Machoke, and Machamp, I'd say that they would fit better into the Humanoid category, as that is where they would seem to fit. But then again, humans are a species of primate, so one could argue that the primate and humanoid categories should be merged, but I digress.
After doing some thinking, I would argue that Mew is some sort of bacteria or amoeba, considering the fact that it can change it's form at will (a trait that it shares with the Pokemon Ditto, who, from appearance, one would guess would also be an amoeba) and is described as the 'origin of all common Pokemon', one would guess that it shares common traits with all species, ergo being the first living organism on the planet, similar to the theories that bacteria and amoebas started off animal life on our on planet.
As for Celebi, Jirachi, Cleffa, Clefairy, Manaphy, Clefable, Mawile, Phione, Happiny, Chansey, Blissey, and, to some extent, Igglybuff, Jigglypuff, Wigglytuff, Togepi, Togetic, and Togekiss (although the later three seem to be more like birds, while the former three seem to be rabbits) would require their own, unique, family. Considering that they show little to no common traits with other Pokemon, I'd guess that they would fit better into their own family.
Now this brings up another problem, considering that Charmander and Charmeleon appear to not be dragons at all, but rather, lizards. Shouldn't they be in listed in the Lizard category, while Charizard is listed in the Dragon category?
I also think that Milotic and Gyarados should be in the Snake and/or Dragon categories respectively, while their pre evolutions should be in the fish category. Considering that the legend that they are based on depicts a small and weak fish climbing up a waterfall, and transforming into a giant sea serpent/dragon.
Another problem arises with the Big Fish and Fish categories, and this problem being Sharpedo, Mantine, and (although it is another tier), Garchomp. The are based on Chondrichthyes (which I probably spelled wrong), a form of cartilage based sea creatures, classified in a separate category than fish, meaning that these three (along with their pre evolutions) should have their own category, separate from the fishes.
And, as one final thing, what about ghosts? They don't seem to be animals, fung
us amongusai plants, or bacteria, so where should they go?