Derek and Angie burying the hatchet at the end of episode 1-8.
In the Japanese version, the end of that episode's operation is the shift where Angie stops referring to Derek as "Tsukimori-san"note Mr. Tsukimori and starts respectfully referring to him as "Tsukimori-sensei"note Dr. Tsukimori.
Derek choosing to join Caduceus over staying at his old hospital, because even though he loses the close patient-doctor relationships that come with working at a local facility, he believes that the potential to save far more lives as part of a major medical organization outweighs the drawbacks.
The end with Derek and Angie reading the letters from the children that they saved in the last chapter was a very sweet way to end the game.
At the end of Chapter 6-4, after you save Derek:
Angie:(teary) ...Thank you...Naomi. I'm sure Derek will get well...soon...
Naomi: I was just doing my job; no need to thank me. ...But, why would you want to hide your tears from him? You think he doesn't already know? That man deserves to see how you feel.
The final scene with Derek and Angie during the epilogue when she finally decided to implicitly confess her feelings for Derek was terribly cute. Especially considering how rockily their relationship started off in Under the Knife and Second Opinion, the duo have really come a long way.
Naomi hugging Alyssa at the end. With everything she had gone through in the series, she deserved the happy ending she earned.