At first, it seems contradictory that the king ordered his men to find The Girl Who Fits This Slipper in the first movie but is the one who points out the plan's flaws in this one. But then consider the fact that the night of the ball, the king was drunk off his rocker, in hysterics, and desperate for his son to get married and make some grandkids for him. His state of mind led him to twist his son's words into a court order, but he sobered up by the next day and could think his plan over on a rational level. And yet even when he admitted his own plan had its gaping holes, the prince still wanted to go through with it.
Take a look at the painting of the queen. Then look at the pocket picture that the King has. They look like Cinderella and Anastasia respectively. You could pass this off as the painting being a dramatization of the pocket one. But the pocket picture only appears after Lady Tremaine does her spell. It was as if the painting was a prediction that the Prince would marry Cinderella.
While it may seems to be an animation error at first, Lady Tremaine destroying Cinderella's dress with magic when she teleport her inside the cursed coach makes sense when you realize that she wants to destroy any hope and dream the girl has from her magic night in the first movie.
The original movie showed Anastasia's a Dreadful Musician when it came to playing the flute, while this movie reveals that she has a very decent singing voice, especially compared to Drizella. This seems ironic, but it actually fits Lady Tremaine's controlling nature very well, and shows that while she's less abusive to her biological daughters she's not a good mother to them. She doesn't really care if her daughters get to do what they like or are good at, long as they do what they're told. She's decided that Drizella should sing and Anastasia should play the flute, and it doesn't matter in the least if this actually fits with the girls' individual talents or not.
It's established early on that magic is blocked or deflected by metal, and Prince Charming uses this to reflect Lady Tremaine's final spell back at her during the climax. That might seem like a bit of an arbitrary cop-out, but it actually makes perfect sense: this is fairy magic, specifically, that we're talking about here, and one of the classic weaknesses of the Fair Folk is metal, specifically iron.
When Cinderella is banished, she's put on a ship to be sent off to a distant land. Just think about that a moment, a young beautiful girl stuck on a ship full of rough sailors who probably don't see women for as long as a month at a time.
The thought of Anastasia having to live a lie for the rest of her life if her mother's plan had gone through. Especially if the second plan had worked, when she's disguised as Cinderella. If they ever consummated the marriage...that's technically rape.