This movie's version of Luigi acts a lot as if Wario was on Mario's side. (Interestingly, this is the only time Luigi doesn't wear green.)
Also, all the Toads were female, at least those who were rescued.
Unlike the other variations of Bowser in the games, this one is clearly a Stalker with a Crush with a very kind and almost innocent personality. But this is Bowser we're talking about.
Ass Pull: The reveal that Kibidango is actually Peach's fiance, Prince Haru.
Broken Base: The ending. Some people actually don't seem to mind that Peach was already engaged with Prince Haru, finding it to be a clever (if abrupt) subversion of the common "Gets the girl in the end" cliche. However, as you might've noticed from the other tropes listed here, others were absolutely furious since Mario went through all that trouble and the revelation came out of nowhere.
The scene where Luigi and Mario getting out of the cave. Immediately after Luigi squeezes out of the hole he dug, he runs back in the cave, which is sealed by a wooden gate, and tries to hide from the Hammer Bro. By running through the gate and breaking it.
Die for Our Ship: Going by YouTube comments, Prince Haru comes under fire a lot. Anger and sadness can do that to otherwise stable fangirls and fanboys.
Ear Worm: That song that plays over the opening credits.
In Mario's fight with Bowser, at one point, he grabs Bowser by the tail and throws him away. Guess what you have to do in Bowser's boss battles in Super Mario 64. Additionally, one scene in the film also involves Mario entering a sunken ship, just like in Super Mario World.
This film used the idea that Bowser is in love with Peach years before Paper Mario 64 practically made it canon. What's more, a plot with Bowser kidnapping Peach with intent to marry would later be canon in the games.
Luigi in this film wears yellow and is obsessed with money, just like the later character Wario.
It's not as egregious as Bowser, but Peach is voiced by then-popular J-pop singer Mami Yamase. The fact that she's an idol and not an actress is apparent, and not helping is that she makes the seemingly adult princess sound like a petulant, nasally ten year old.