The turtles being extremely protective of April when they meet Casey, with Raph throwing his sai at Casey and outright blocking April from view when she's talking to the others.
Splinter is still called "Dad."
April jumping in front of the cops, who had Raph and Mikey at gunpoint, and willingly getting arrested rather than let the turtles be captured.
The fact that Casey does this as well, having only just met the turtles. While April considers the turtles family, this shows that Casey is a truly good person willing to risk his life to protect the innocent.
When Leonardo storms off after a heated argument with his brothers Splinter steps up and reprimands him (albeit in a very subdued and concerned manner, as a loving father) about trying to force the rest of the group to think and act like himself. He points out that as their leader and brother, Leonardo should understand and accept their differences, since they make them stronger as a team. Leo takes his father's words to heart and, for the rest of the film, makes genuine effort to connect better with his brothers and let their individual traits flourish.
A small blink and you'll miss it moment, when Mikey innocently assumes that Bebop and Rocksteady have achieved the power of flight Donatello gently corrects him that they're simply on a plane. Leonardo can be seen out of focus in the background giving Mikey a fond smile, probably pleased to see him regain his joy again after seeing that he was on the verge of tears a few minutes ago.
Despite the fact that the brothers' relationship had been strained because of the purple ooze Raph still shows concern and genuine terror when he sees his brothers jump off a plane without any parachutes on.
Raph: Wait! You don't have a chute!
A subtle but nonetheless heartwarming detail. During the trip to Brazil, Donnie shows genuine concern for his immediate older brother whenever he doesn't see Raph among their group. First is when they've all jumped on to Bebop and Rocksteady's plane and the second is when they all fall into the river after the plane crashes.
Donnie: Wait, where's Raph?
Raph's protective big brother instincts for Donnie kicks into high gear when a tank missile is launched at the purple turtle. Raph sounds utterly panicked and fearful when he screams Donnie's name while pulling him out of harm's way.
Unlike with previous incarnations where Mikey is only treated as the funny guy and annoying little brother, here the brothers genuinely treat him as a member of the team and rely on him for very important tasks. During the high speed chase scene in the garbage truck, Donatello gives Mikey charge over the weapons and specifically designed them to be nunchucks, Mikey's signature weapons. This is surprising since Raph would seem like the better fit for handling weapons of mass destruction and even complains about it. When Shredder is about to escape, Mikey is the one who maneuvers the net cannon under Leo's orders. Leo is aware that they only have one shot to catch Shredder and it is Mikey that he trusts with this important task. Later when infiltrating police headquarters, Raph relies on Mikey's hacking skills to get April through security. And in the final battle against Krang, Leo calls for Mikey to get the beacon that is assembling the technodrome while he and Raph fight Krang.
Bebop and Rocksteady's loving bromance is both funny and sweet. They really do care about each other. Particular moments that stand out are when Rocksteady saves Bebop from falling in the river again.
