A minor one but in the first episode when Treville arrived to arrest Athos, Aramis and Porthos immediately place their hands on their swords, prepared to fight if needed for their friend.
The scene between Constance and Aramis during the rescue of baby Henri in 1.06 is an equal mix of hilarious, heartwarming and awesome. Aramis sings a lullaby to the baby and while he rocks the child he performs a little dance. Constance's irritation at Aramis continually undermining her hard won revelations about the baby's grandmother is also cute. And when Constance defends the Musketeer and child with Aramis' sword, the reactions of both Aramis and the enemy mook that she trounces are absolutely priceless.
"I would ask you to come with us ... but you already have a family."
D'Artagnan finally becoming a Musketeer in 1.08. He visibly tears up as King Louis inducts him into the Regiment.
In 1.09, after spending half the episode flirting with the daughter of a high-ranking German chancellor, and drunkenly complaining to Richelieu that he 'wishes the Queen was dead' so he can remarry and finally produce an heir (which was all the excuse the Cardinal needed to try to assassinate her), the subsequent reunion between King Louis and Queen Anne after her rescue is one of the few moments we see where they do care about each other on some level.
Most of 1.10 is made of this. D'Artagnan calls Athos his best friend when refusing to kill him for Milady. The Musketeers laugh at each other and 4-way hug after a fight, and Porthos tears up at Athos's fake funeral. Even though he knows it's fake.
"One for all. All for one."
Louis's unrestrained joy when he sees his possible son for the first time.
In a subtle Call Back to another infant "of royal blood", the lullaby that Aramis sings to the Dauphin in 2.02, is the same one he heard Agnes sing to baby Henri in 1.06.
Bonacieux telling Rochefort that he doesn't know Constance's location after they find out that she has taken the Dauphin. Prior to this, she'd begged him not to tell anyone that he saw her and refused to tell him why she was carrying someone else's baby around town. He has no reason to do what she asks (considering he knows she had an affair with D'Artagnan and was all too happy to leave the inn and stay in the Palace as the Queen's confidant), but he still does it anyway.
Before this, he actually looks happy when he notices her and asks if she's come to visit him.