Before April changes her disguise she is wearing a black skirt and full length stockings. She puts a new skirt on over this which is not long enough to cover the black one. She makes no other adjustments to her costume below the waist. Suddenly the first skirt has vanished and her stockings are only knee-high.
In Bebop and Rocksteady's transformation scene, Bebop's boots are shown to be destroyed due to his feet growing with the mutation. However, when he's seen just after the transformation, his boots are fully intact.
When April changes into a school girl's outfit to distract Dr. Stockman's assistant, she grabs a miniskirt and ties it around the skirt that she's already wearing. But we never see her take this particular skirt off. It just magically disappears. She is also wearing pantyhose which suddenly changes to over the knee stockings.
When Bepop and Rocksteady are at the Horseshoe bar talking about climbing up since Shredder is out of the picture, when filming from the right side Rocksteady beer mug is half full. When filming from the left side there is only 1/10 of mug filled.
The video introducing Vern at the basketball game includes a progression of newspaper and magazine headlines to summarize the events of the previous film, but the visible dates on some of the publications bounce back and forth totally out of order between July 2014 and December 2013. Also, the video begins by saying the events happened "a year ago" but the game is being played on October 31st, which is significantly more than a year after the latest publication dates of July 2014.
When April is running with the canister, she has it in her right hand. The part where she has to put her hands on the car, you see it go from her right hand immediately to her left hand in the next shot.
When we first see the Technodrome building itself and Donnie is analyzing it on his computer, we see a number on the screen slowly counting upwards. In one shot the number is in the 331,000 range. A few shots later, it passes by this number again.
When the turtles are shown on a cargo plane returning from Brazil, it is a night scene, but the scenes in New York just before and after the exterior shots of the plane are set in the daytime on the same day, and they arrive back at their lair on that day. The only way it could be light in New York and dark in Brazil is if their plane departed shortly after sunset in Brazil. But by the time they got to New York, the sun would have set there as well, so it should have been night, not day.
According to Dr Stockman, Bebop and Rocksteady's new forms are due to dormant genes connected to humanity's animal ancestors. This is partly correct, though clearly not in the way intended: every gene, dormant or otherwise, connects us to our ancestors. But humanity's ancestors do not include rhinoceros or warthogs.
When Vern goes to get recording from a hidden camera in a wall clock, he had to pull out whole wiring from the ceiling/wall and it returns to point just below where actual hidden camera was placed/installed.
What electrician/technician would waste such a long wire around the hall if had to put the storage device just below it. (May be until he wants to offer big bill to earn more)..
When April uses Chief Vincent's phone to call Vern, the time on the wall clock in the interrogation room is 6:10. Since she and Casey were arrested a few minutes after 10:15 p.m. (according to clock in police HQ locker room), it is presumably 6:10 a.m. because following the phone call, Vern visits TCRI during the noon hour. However, sunrise in New York City on November 2nd (the date of this scene) isn't until 7:30 a.m., so it should have been dark outside Vern's window.
Pre-mutation Bebop is clean-shaven. As part of the mutation, he grows additional hair out of his ears, near his mouth, along his spine and from the tip of his new tail. All of this new hair is purple, which would only be possible if that were his natural hair colour.
For most of the film, Krang seems to have complete control over his robot body by a direct neural interface. Except at the end of his first conversation with Shredder, when he switches to giving it verbal orders for no apparent reason.
In the first film the shredder is bald and is covered in scars while in this film he has a full set of hair and has much less prominent scarring. However, he survived the climax of the previous film only by exposure to the mutagen's regenerative effects. Apparently that included healing his old scars as well, and even seems to have made him younger.