"Rise of the Turtles pt. 2" After recounting the tale of how he lost his wife and daughter, and Leo agreeing that he lost much (he is no longer human), Splinter says that he had gained much as well- his four sons.
After Kirby decides to cover the turtles' escape from the Kraang's base, and, as a result, gets left behind (which is something of a moment in and of itself, since April's watching it all happen). Devastated, April hugs Donnie, who goes on to reiterate that they'll get her father back. It's still on the sad side of heartwarming, but says a lot.
Any scene of Mikey bonding with Leatherhead, starting with Mikey feeding him "pizza noodle soup". Then after Leatherhead talks to Mikey about what a dangerous monster he is, Mikey says "Maybe you just think you're a monster because everyone treats you that way." Maybe he really is wise beyond his years.
Raph's worry when Mikey is knocked out when they're fighting Snakeweed. He doesn't even try to hide his relief when Mikey finally comes to.
Also, Raph shouting Mikey's Catch Phrase "Booyakasha!" as he delivers the final blow to Snakeweed, for the same reason. Doubles as a Moment Of Awesome.
Especially heartwarming when, back in the layer, Raph says that he has no problem risking his own life, but not his brothers.
Karai choosing to help Leonardo escape from Snakeweed instead of letting him die. Especially notable since Shredder had already given her a stern warning that she wasn't to let him live the next time they met.
Leo saving the knife she threw at his head as a memento at the end of the episode.