These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Lipped Alligator Moment: When the 1987 and 2003 Turtles visit the 1987 universe for the first time, they witness the 1987 Turtles getting into a battle with a giant mutant banana, pizza monsters, evil leprechauns, and monstrous bowling balls, saving 1987 April in the process. After this scene, the Turtles leave, and 1987 April is abducted by a mutant banana, never to be seen or referenced in the movie again.
Broken Base: Apparently, the movie's treatment of the 1987-verse divided some of the older show's fanbase. For instance, Doug Walker liked the movie enough that he threw out the causticCritic persona and praised it out-of-character; by contrast, Walker's fellow reviewer Phelous was one of the few internet critics to give it an overwhelmingly negative review.
Complete Monster: Whilst not a trait unique to this movie; 2003 Shredder really crosses the line here when he decides to kill everyone in the known universe, including himself, and doesn't have any intention of stopping even when Karai, his own daughter, begs him to. It's little wonder all love and loyalty Karai has for him ends at this point.
Creator's Pet: Some fans accuse the '03 Turtles of being this, seeing how the '87 Turtles were pretty much Straw Losers to them.
Hilarious in Hindsight: Mirage Leo's narration works even better as a parody of Frank Miller's work now than in the late 80's.
Ho Yay: 1987 Shredder when describing Ch'rell, and later Krang's little comment when they located him... it's in the tone of their voices.
Moral Event Horizon: 2003 Shredder does it again, as he callously attempts to murder the Turtles by using them to pinpoint Turtle Prime. Granted, he's tried to kill them hundreds of times before... but not while Splinter was watching them die, yes, the other Shredders have attempted this, but there was no real sign of a Deus ex Machina, Chekhov's Gun, or really anything this time that could save them except somebody from the outside, this is what gets Karai to finally switch sides for good.
Nightmare Fuel: 2003 Shredder's plan. Destroy the entire universe? Watch as the entire world erases itself, everyone in it and any loved ones you may have before being erased yourself? Pretty frightening.
There were a few other examples, such as Hun's quote in one scene.
Hun: Yes... Mutation, it's a real horror show.
In story example: the Mirage Turtles were this to the 1987 Turtles, who were so afraid of their "willing to kill, dismember your body parts and do it with a smile" counterparts that they dropped their weapons and fled. Hell, even Ch'rell was afraid of them when they got up-close and personal.
2003 Raphael and Leonardo's conversation with the 1987 Splinter.
Especially in the Uncut version, because that scene references a (deleted from the original) scene where the 2003 Splinter voiced similar sentiments. It seems that no matter where in the Multiverse you go, Splinter is always a rock of stability and calm for the turtles.
Seeing the supporting cast of the 2003 series being erased, along with their world.
Villain Decay: This Trope was inverted for threats from the 2003 such as Hun, who mutated into a Turtle monster, while this condition isn't exactly liked, he actually becomes much more powerful, so powerful, in fact, that none of the Turtles can defeat him.
Played very straight with Shredder and Krang, who went from goofy but somewhat menacing in the '87 show to entirely useless here.