Plot hole: Splinter knew all along the name of the company who made the Ooze, and literally sat on this vital piece of information for over a decade just because he was too stupid to simply look the name of the company up, written on giant letters and far from being hidden - he merely had to open the yellow pages, no doubt. Nobody with such a telling piece of evidence about their own origins (the canister that mutated them is in his hands and has the logo of the company with the name spelled out) would be unable to find out something this obvious. (00:22:00)
Plot hole: Throughout the movie, the strength of the two beasts fluctuates heavily; they can chew and break telephone posts with ease, they can toss a Turtle many meters in the air through a roof, but they are caged by makeshift cells of junk poorly pieced together or a little horse trailer. (00:39:30)
Plot hole: Shredder unleashes Tokka and Rahzar in a residential part of New York. The time is not stated but two senior citizens are taking a cab and there are a cafe and other stores open, it's not quite the middle of the night. Yet the police and the journalists are on the case only the morning after in full daylight. (00:59:45)
Plot hole: The timeline of the movie is quite strange; April obviously got her job back and made advancements in career, living in a sweet two-floor loft. At least -some - time must have passed, many pizza deliveries and all that, but Shredder just woke up from the pile of garbage he ended in at the end of the last movie and the Foot hasn't attempted any reaction or organization yet, implying it is set mere hours after the first movie.
Plot hole: It's never really addressed or explained how Shredder survived his death in the previous movie from being crushed in a garbage truck.
Suggested correction: It didn't really need to be addressed, and thus is not a mistake. His hand emerging from the junkyard is enough to show that he survived his apparent demise at the end of the last film.
