WMG / The Sword in the Stone

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.
  • Wart mentions slaying dragons as a knightly duty, and does so casually as if it's a common occurrence, lending credence to the idea that they do exist in this universe.
  • When she made the rule against disappearing, she meant disappearing as teleporting away instead of becoming invisible.

Madam Mim was watching over Merlin and Wart the whole time, and caused the Pike incident

This deleted scene shows that 1) Wart is well and good King Uther's mysteriously disappeared son, and 2) Madam Mim is the only one in the land besides Merlin who's aware of that. You may not agree, but I want to take it as canon. (After all, we do not find out in the finished version what Arthur's origins really are, do we?) From that point, I think Madam Mim was causing all the troubles that happened to Merlin and Arthur.

First, following the deleted scene, she caused Kay's arrow to get lost in the woods (though this turned out as a good thing later, which must have unnerved Mim immensely). Then she shapeshifted into the purple catfish Merlin and Arthur bump onto in their fish form. I mean, purple catfish ? Madam Mim was clearly spying on them. Just to cause trouble for Merlin she likes to see Merlin in trouble, whether she actually gains anything from it or not -she transforms some harmless fish into the ferocious pike that attacks Arthur and Merlin. "What in thunder is a monster like that doing in the moat?" asks Merlin. Well, ask Madam Mim and see what she has to say.

Then she became the fat squirrel that tried to court Merlin. She too was purple, remember? The squirrel lady that troubles Arthur was a genuine squirrel, but Mim, who was spying on Merlin and Arthur, immediately sees the potential of this kind of troublemaking and decides to try it. On who? On Merlin, of course! She'd just love to see Merlin's embarrassed reaction to that.

I put emphasis on the fact that Mim does all that more to trouble Merlin than anything else. She doesn't care if Arthur becomes king  well, as a Card-Carrying Villain she likes the Dark Age as it is, so if you ask her she wouldn't be that favorable to Arthur being crowned, but she doesn't feel personally concerned. She only starts to interest herself in Arthur himself when he happens to fall in her house in bird form.

  • (Though I hesitate, perhaps she caused the hawk to chase Wart to her house.)

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. Alternatively, Guinevere had been cursed as a squirrel by Mim, and the bigger squirrel is her handmaiden so Merlin simply removed the curse.
  • If this be the case, then it's very likely their direct descendent was..Squirrel Girl.
  • Original Troper: I wasn't aware the legend Guinevere was unfaithful to Arthur.

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 and Madame Mim went to Hogwarts.
Even though this film was released decades before Harry Potter was published there is enough evidence to suggest Merlin and Madame Mim are former Hogwarts students. Merlin was probably a Ravenclaw as he wears blue which is one of the colours of Ravenclaw. He is very wise again suggesting Ravenclaw and prefers education to fighting again Ravenclaw. It is also possible Merlin's best subjects were Transfiguration as he is able to turn himself and Wart into all kinds of animals. He was also probably top of divination as well as he could tell what time Wart was first coming to his house and knew Wart was the future King Arthur and what the world will be like in the 20th century. Mim meanwhile was a Slytherin as she easily broke rules that she made and seemed to process dark magic as well. Like Merlin she likely excelled in Transfiguration as she can turn into not only animals but a hot looking girl as well. Plus both characters can perform non verbal spells especially when turning into animals and both can do magic without wands. This would imply both had very high grades at O.W.L and N.E.W.T level. But the pair unlike other witches and wizards live in the muggle world and it would explain why Sir Ector refuses to believe Merlin can do magic.

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 Lord
His magic is just really advanced technology. And of course he travels through time.
  • Adding credence to this theory is the fact that he also seems immortal, like Madam Mim, based on both of them making frequent appearances in Disney comics set in the present day.

Vernon and Dudley Dursley are expies of Ector and Kay.
It's said at the character page that Rowling herself considers Harry Potter an Expy of Wart. Kay is a medieval version of the adult Dudley would become if not for the dementors.