Before the song "One Small Thing" when Twilight was getting the others to help Skystar, Applejack is an odd color.
During the song "We Got This Together" when it goes over the table to Big Mac, Golden Delicious's eyes are green but when it cuts to the wide shot going over to Rarity his eyes are blue.
When Tempest was in the throne room the positions of the princesses was Celestia top left, Luna bottom left, and Cadence top right. But when Twilight is captured Celestia is in the bottom right and Cadence is in the top left. And near the end of the movie when the princesses are no longer Celestia is back in the top left and Cadence is now bottom right, Luna never moved.
When the Mane Six fall from the broken bridge into the water below, Pinkie and Twilight fall down backwards in a horizontal position, Rarity on her sides in a horizontal position, Rainbow is spinning in a horizontal position, Fluttershy is slightly spinning in a horizontal position, and Applejack forward in a horizontal position, but in the next scene, Pinkie and Twilight are now upside down in a vertical position, Rarity is right side up in a horizontal position, Applejack and Rainbow Dash are upside down in a horizontal position, and Fluttershy's horizontal position is reversed 180°, and considering Fluttershy and Rainbow Dash were the only ones moving, there is no way the other ponies would have moved that quickly, Pinkie would have had to rotate 90° and Twilight 180°.
In the song "Open Up Your Eyes", Tempest Shadow says "Don't ever count on anyBODY else" instead of "Don't ever count on anyPONY else"
At various times, Rainbow Dash and Fluttershy, having wings, forget that they can fly.
When Pinkie Pie surfaces from the water saying "She's gone!" her mane is still dry.
When the magic of the alicorns and Equestria is being restored by the Staff of Sacanas, the spot where the Storm King fell is shown but the pieces of his shattered stone-self are missing. The animators had most likely forgotten to add them in before fully completing the scene.
Even though Twilight Sparkle has a magic unicorn horn that she can use to cast spells and it is shown she can do so in the show, in this film, with the exception of her lighting up a cave, catching a petrified Luna in mid-air and lowering her safety to the ground, and assembling a hot air balloon in mid-air, she never casts any spells nor uses teleportation at all.
In the show, the way the sun and moon move are by Celestia and Luna moving it, but it still changes from day to night when the Princesses are turned to stone, unable to move.
During the invasion; princess celestia tells Luna to get the help of the hypogrifs. once Luna is incapacitated; the mane six go. however; it is never explained how the hypogrifs are going to help or why it has to be them.