Apparently Shredder isn't Shredder, but "Colonel Schraeder," and those are his "F.O.O.T." Soldiers. That's why he can be a white guy, and why the Foot look like paramilitary. In the third act, when it's revealed that the turtles are not actually turtles but the four "chosen ones" from Dimension X's widespread humanoid turtle species rather than the accidental mutations that Splinter had always told them they were, it's also revealed that "Schraeder" is from the same dimension they are. He can sprout blade-like protrusions, leading Michaelangelo to say "more like 'SHREDDER!"
The story focuses on Casey and April, using the turtles as background props a la Transformers. April jumps on a trampoline. Hilarity ensues.
This is so crummy. It's easy to see why Nickelodeon/Paramount allowed Bay the franchise - he made a killing with those POS transformer movies. It might make money, but it's barely a story, it's unfaithful to the source material, and it sure isn't art. Thankfully, we'll always have the original comics and the new cartoon. That new show on Nick is actually probably the best possible mainstream interpretation, combining the best aspects of all previous versions of TMNT and taking their time to tell a story. I'm interested to see what the mocap turtles end up looking like, but I'll most likely skip the film.