This article is based on my opinion and first movies only. Not all of the Disney Princess villains did a big mistake. But there are 3 villains who, I think, made the greatest mistakes.
3 Villains Who Make the Biggest Mistakes
Yes, she wants to kill Snow White secretly. She transforms into a scary old hag that Snow White doesn't know her. But she makes one great mistake: putting poison into the apple which has love's first kiss for an antidote. Doesn't she see perfectly that Snow White has a lover: the prince? And she makes an assumption that the dwarfs will bury Snow White alive. That's only her presupposition. The dwarfs don't bury her alive, do they? 2 mistakes of the Evil Queen: giving poison that HAS an antidote (and she knows Snow White might get that antidote -- love's first kiss) and assuming that the dwarfs will bury her alive.
Jafar almost wins when he gets the Genie of the lamp. He becomes Sultan, he has the palace for himself, and he takes Jasmine and her father captive. When Aladdin attacks him, he's just a street rat he might have easily crushed with such powers. But he makes ONE BIG MISTAKE. He listens to Aladdin, who is his enemy! Aladdin says he's just second-best, and he believes it. How very stupid of him. Come on, Jafar, Aladdin is your enemy! An enemy is looking for your downfall. And you listen to him?
Gothel has lied about many things to Rapunzel: she pretends to be her mother, she says the outside world is full of people who wants to take her hair, etc. But why does she tell Rapunzel the truth about her birthday? If she doesn't, Rapunzel won't suspect about the floating lights that only appear on her birthday. Perhaps, because Rapunzel is smart, she'll wonder about the lights that come once a year, but it's not her birthday. She'll have to solve a harder puzzle than that!
Well, I guess the other villains make mistakes too. Else how can the heroes and heroines defeat them? Hahaha. But I think their mistakes are not so great. Perhaps it's the heroes and heroines who can outsmart them!
I think she doesn't make many mistakes here. She has neatly locked Cinderella in her room, she has almost succeeded in getting the Duke away from her mansion, she even has broken Cinderella's slipper! It's just the mice are sneaky enough to slip into her pocket and take the key, and of course Lady Tremaine doesn't suspect Cinderella has the other slipper.
Does turning into a dragon count as a mistake? Hm... I'm not sure. Being a dragon makes her more easily seen, while as a fairy she can just disappear. But maybe that's not what she thinks. Being a dragon is more scary and powerful. She can breathe fire over Phillip! I can only say that the Sword of Truth and Shield of Virtue that the good fairies give are stronger than Maleficent's fires.
Perhaps Ursula's mistake is unawareness. She transforms into a giant version of herself when she gets Triton's trident, and she tries to kill Ariel with the trident, but she doesn't notice Eric steering the old ship that was going to pierce her.
Gaston is the key to his own downfall. After stabbing the Beast, he lets go of the railing and falls by himself. Well, I think Disney made him do it so that the Beast doesn't kill anybody (same as Tarzan doesn't kill Clayton, Clayton gets hanged by himself).
After causing the war between the Native Americans and the Englishmen, Ratcliffe creates the mistake of shooting John Smith. It shows his greed and impatience. The Englishmen, led by Thomas, turn to attack him instead.
He's one of the greatest DP villains in my opinion. He's lost most of his soldiers in that avalanche, but he still manages to occupy the Emperor's palace with only 5 men! I think he doesn't make a mistake at all; it's Mulan's sharp wits who defeat him.
Of course, his biggest mistake is trading his soul to the evil spirits. Facilier lives in fear: he's afraid when he loses Naveen because he needs Naveen's blood; he's afraid that his plan doesn't work and he has to pay his price; and finally he's afraid the talisman will be broken, like in the final scene where Tiana smashes it and Facilier gets pulled by the evil spirits. But if Facilier doesn't trade his soul to the evil spirits, he won't be a villain at all!