Madam Mim was playing by the rules the entire time.A point in The Sword in the Stone is that Madam Mim apparently cheats to get ahead of Merlin in the Wizard's duel. But, perhaps, she didn't, and is merely a more brilliant fighter than Archimedes gives her credit for. One would imagine the penalty for cheating with magic would be devastating to the cheater. First, she pulls a disappearing act, but who's to say she doesn't do the same thing Merlin did at the end of the fight: Transform into something minuscule to avoid being seen in order to set up for her next move (like a gnat or flea)? The rest of the time she transforms into animals like the rules state, no fireballs or anything crazy like that. And then we come to the Dragon. Merlin claims Mim said no Dragons but, in fact, she didn't. She said nothing make believe like Pink Dragons and stuff. If Lancelot slew a Dragon in the Camelot Mythos, it could be that Pink Dragons are phony...but Purple Dragons are not. "Did I say 'No Purple Dragons'? DID I?!" No, Mim, you did not.
The girl squirrel is Guinevere.After Arthur becomes King, Merlin goes back and changes the squirrel into a girl. After he teaches her to speak English and not bury her leftovers, her introduces her to Arthur and lets nature resume it's course. Alterantively, Guinevere had been cursed as a squirrel by Mim, and the bigger squirrel is her handmaiden so Merlin simply removed the curse.
Wart was not "destined" to become the king.The sword responded to him because of his motives for pulling it. All the men who had tried in the past did so because they wanted to be the king and rule over England. Wart did it in order to replace Sir Kay's sword which he had forgotten at the inn—in other words, to correct a personal mistake and fulfill a duty of service which he had taken on. Thus he marked himself as the kind of king England needed—someone who would serve the people and strive to right wrongs instead of just lording it over them like the current crop of warlords.
Merlin decides never to turn himself or anyone else into squirrels again, because it just makes everyone miserable.Both in hilarious and heartbreaking ways.
Merlin brought Wart to the squirrel because he knew about his future with Guinevere.He laughed and enjoyed seeing Wart deal with the unwanted affections of a squirrel. Deep down, he knew of his future heartbreak from his wife, and wanted to show Wart what heartbreak was like to help him prepare for it when it came.
Merlin is a Time LordHis Magick is really advanced technology. And of course he travels through time.