Also they did decently with the idea that the mushrooms would be everywhere.
And Mario's jumping ability was given the somewhat-plusable explanation with the boots.
And the use of the Bob-omb.
Where it starts to fall apart for me is the backstory they came up with for the movie:
"The Meteor that killed off the dinosaurs, also split the Earth across dimensional lines, and in their universe, Dinosaurs had convergently evolved into humanoid figures that somehow drained the planet of all of its resources, causing run away desertification in the process.".