Charles Perrault's version of the Fairy Tale mentions that one of the step-sisters was not as mean as the other one which explains Anastasia's redemption in the sequel and threequel.
The third movie was the first time Cinderella had something serious to fight for and was in actual danger. It makes sense that she'd be more badass than in the original movie.
Lady Tremaine and her daughters are the most infamous cases of Karma Houdini in the Disney franchise (unless if you count the third film). In the original Perrault story, Cinderella forgives her stepfamily.
Cinderella's name choice for Gus. ("Now for a name. I've got one! Octavius. But for short, we'll call you Gus.") That's because Gus is actually short for Augustus. In ancient Rome, Octavius was renamed Augustus when he became Caesar. Hence Octavius - Augustus - Gus.
When Cinderella was confronting her stepmother for the prank that her stepfamily assumed she did, look at the lighting and use of shadows when Cinderella is still inside her stepmom's room, still near the door: they resemble prison bars. In other words, Cinderella is in her own prison.
Why the big deal with the glass slipper fitting the girl? Why not just have the prince identify his love? Well, the prince probably was out searching for Cinderella. But it's a big enough kingdom and literally every eligible woman was at the ball, so he needs help tracking her down. The Duke gets stuck with slipper duty because he doesn't know Cinderella's face as well.
Most claim Canon Discontinuity when the king orders "girl who fits the slipper" hunt in the first film but lampshades its ridiculousness in the third. However, he was in hysterics, and possibly even drunk, when he made that order. So it is likely he had a clearer head by the next morning and would've called the order off had his son not insisted they keep trying.
He lampshades it even in the first film. He wants his son to marry, so he goes down the Exact Words route. The Duke says that the shoe could fit any number of girls - and the King says that the Prince will have to marry whichever one the shoe fits.
As pointed out on the Headscratchers page, searching via the shoe is actually quite a reasonable idea. No internet or TV to track her down - and she definitely didn't get an introduction at the ball. But a shoe made of glass would have to be moulded around the foot to be an absolute perfect fit. If Cinderella has unusually small feet, then she's probably the only one who could fit into it. So searching via the shoe has a good chance of finding the right girl (provided her stepmother doesn't lock her in the attic that is). Also, although unknown to the prince, it's a magic shoe, so it could fit only Cinderella and be suitable for dancing in although made of glass.
In Real Life, a Grand Duke and a King are often related, often as closely as cousins. No wonder the Duke can speak so open-mindedly to the King - they are close relations!
As much flak as this movie and the Cinderella story in general gets for the heroine only waiting for things to get better without her improving them, Cinderella here does at least try to help herself. She asks if she can go to the ball, intending to make her ballgown herself in a single day (though her family plays on Exact Words and keeps her too busy to do it, leaving the job to the mice and birds), is the one to tell the mice to get the key when she is locked in, and perhaps most importantly, kept one of the glass slippers hidden, providing irrefutable proof she is the one from the ball (the shoe could have fit several women as pointed out, but only the real owner would have the other half of the pair after all.)
Look at the stepsisters' feet when they try on the shoe. For one of them, it stays dangling on the big toe, and the other has to arch her foot to fit in. In the Grimm version, one cut off her big toe, the other a part of her ankle, and it was the blood that gave them away.
When Cinderella was fleeing the ball, her carriage barely managed to get through the doors, and was in the process of very nearly outrunning the riders chasing it. Part of that can be explained by a magic carriage being particularly light and fast. However, it takes a very experienced coachman to handle the horses correctly and take full advantage of the carriage's maneuvering power. Cinderella's godmother very intelligently chose the old family horse, who had likely pulled plenty of carriages in her family's heyday, to drive the carriage. The footman, a tenacious and smart-looking fellow who has to be loyal and alert to his nobility's every need, was the dog. (This was pure Disney. In Perrault's version, the coachman was a rat and the footmen were lizards, and Grimm's story doesn't have a coach at all.)
If Cinderella did not escape her room in time, what would Lady Tremaine have done to her? Leave her in there to starve to death? Kill her when everyone left?
Cinderella's step-sisters destroy the dress she's wearing with their bare hands after discovering that she made the dress out of the same materials they had on their dresses. A kid is reminded of fighting with her own siblings over things like clothes and thinks, "That's so mean!" An adult finds it disturbingly similar to sexual assault (or, if you really want to be perverted, a good, ol'-fashioned, clothes-rippin' Cat Fight).
More Fridge Horror comes in when you realize that if the stepsisters have no problem assaulting Cindrella in such a fashion (no pun intended), then they and their mother may have physically abused Cinderella prior to this!
The worst part? That dress was all she had left of her dead mother!
Maybe that's why the dress only has a few rips in the 2015 version. Ella could get a needle and thread and fix it.
In Cinderella: A Twist in Time, the lengths Lady Tremaine goes to replace Cinderella with one of her own daughters as the prince's wife is really alarming, when you think about it. Cinderella is Happily Married, moved away from her stepfamily, and probably never thought she'd have to deal with them again. Then Lady Tremaine turns back the clock and starts casting enchantments left and right to have her way. Even worse, she's clearly more than willing to erase Anastasia's identity in the process. Her last plan was to turn Anastasia into a copy of Cinderella. So not only was she tricking the prince into marrying under false pretenses, but she's condemning Anastasia to either a marriage as a lie (if Anastasia stays looking like Cinderella for the rest of her life) or a marriage where the prince is almost certainly resentful and upset (if Anastasia is turned into her own form after the wedding).
If you impersonate someone's significant other and have sex with them, it's rape. Lady Tremaine's plan basically encourages Anastasia to rape Prince Charming.
After Anastasia brings home the magic wand, her mother assumes its just a stick and the other sister blurts out "Let's beat her with it!" I guess now that Cinderella is gone, the Mother found another outlet for her cruelty... Even worse is that Anastasia and her sister seemed to be, while maybe not close, at least getting along with each other before...Which means that Anastasia's sister probably turned on her just as fast as their mother did, and probably takes part in the abuse herself!
According to Cinderella, "A dream is a wish your heart makes". If one were to take this to be true, then hearts really love to wish for messed up things, and nightmares!
To say nothing of the fact that Cinderella married someone she knew nothing about.
That turns into more of a fridge tear jerker if you realize she did it to get out of an abusive household.
The King's motivation is to have grandchildren by any means necessary, and he sics the castle guards on Cinderella when she tries to escape and tries to kill the Grand Duke when he explains she got away. What would he do if Cinderella was unable to have children?
In this universe, the Fairy Godmother could probably have turned one of the animals into a child or something.