Bruce telling Alfred he doesn't want him in the field because he wants to keep him safe from harm.
Tatsu still refers to Alfred as "The Major"- her childhood nickname for him when he worked with her father (and possibly his station in MI:6)- even though she's grown up.
Alfred revealing to Bruce that she's his goddaughter.
Batman complimenting Tatsu for solving his test.
Poor Jason Burr's attempts to woo Tatsu and the subtle hint that Tatsu may like him.
He even made her smile a bit.
Alfred and Bruce's talk at the fireplace.
Bruce: I need to find out who's after Burr. Alfred: Perhaps you should search Dr. Burr's lab. Bruce: Thank you, Alfred. You know I've done this before, right? Alfred: And you're getting better at it everyday.
Tatsu saving Batman and considering that he was right about sparing Silver Monkey's life.
The fact that Batman chose to hack Gordon's phone to communicate with him.
Barbara and Jim's interaction at their house.
Batman showing compassion to Humphry when says that he never wanted to hurt anyone. It also shows that Batman truly cares for members of his Rogues Gallery who are suffering from insanity and wishes to help them rather than just lock them up.
Tatsu telling Alfred to truth about why she took his job offer.
Gordon thanking Batman for not staying out of the case.
Humpty Dumpty proving true to his word about not wanting to hurt people by releasing his captives.
Batman comforting Barbara after Humpty Dumpty kidnapped her father.
When Batman breaks into the Gotham PD to talk with Gordon, he doesn't even attempt to arrest Batman or call for backup, which shows he's starting to trust him.
It's small, but when Batman meets a civilian who tells him that two people are trapped in the toy-like machines, one of the cannonballs nearly hits him because of Batman knocking down a pole. The civilian doesn't react angrily, but compliments Batman, knowing that he's here to help.
Sapphire's love for Rex.
A subtle one, Katana was said to be shadowing Dr. Burr's move.
Batman's attempts to help Metamorpho.
Sapphire's defense of her father is all the more heartbreaking when the truth is revealed.
Bruce telling Ravencroft that "I'm glad I'm no longer your patient" on their date. Making it all the more of a Mood Whiplash when it's revealed she's working with someone for reasons yet revealed.
Tatsu selflessly going to save Bruce even after he fired her and Alfred.
Bruce telling Tatsu that she passed the final test and reveals his identity to her.
Alfred: Welcome to the family.
Barbara finally meeting Batman and being happy to know that his partner, Katana, is a girl, meaning that she could possibly join him at some point.