When Mike temporary leaves after a fight with Gloria pertaining to Gloria's pregnancy, Gloria is distaught. So with Gloria on his lap, Archie tells her about the time when Gloria was born.
Archie spends an entire episode dragging his feet about spending the weekend with Edith at the same hotel room they spent their honeymoon on their anniversary. Just when you think he might not even care about her at all, he sees her in her nightgown and is blown away.
Archie: Did... did you wear that dress on our honeymoon?
Edith: No, it's brand new.
Archie: Oh... for a minute there I thought... you look exactly the same as you did that night.
In the episode "Mike's Appendix", Archie pays for Mike's operation and asks Gloria not to tell him that he did. His reason for doing it: "He's the only Meathead you got."
When Stretch Cunningham dies, Archie attends his funeral and is surprised to find out that his old friend was Jewish. Naturally thus leads to some awkwardness on Archie's part, but he ultimately honors Stretch with a touching eulogy.
In the season 8 finale the final moments with Archie and Mike are this mixed with a tearjerker. Archie does everything he can to fight the fact the he's actually going to miss Mike but you can tell by the look on his face that when Mike tells Archie he loves him and will miss him that Archie feels the same way, he just can't spit it out.
Archie is trapped in an elevator with a hysterical woman, an erudite African-American professor, and a Hispanic couple. When the wife goes into labor, Archie of course gripes and grouses the entire time. The range of emotions that play across his face is astonishing—from looking thoroughly annoyed and grossed out at the sound of the woman's screams, then genuinely worried when he asks why the baby isn't crying, then incredibly relieved when he finally does begin to cry. The husband gently invites him, "come and see my son", leading Archie to offer a fumbling congratulations on their little boy.
The episode "Cousin Liz", where Veronica talks (albeit with a lot of confusion and struggle) to Edith about her relationship with Edith's cousin Liz and about how it was "like a marriage". Edith figures out what she means and accepts their relationship.
The episode "Stephanie's Conversion". Edith finds out that Stephanie has been hiding the fact she is Jewish from Archie. When he finds out, he hits the roof but soon has a change of heart. At the end of the episode, he gives Stephanie a Star of David necklace and tells her: "You've got to love somebody to give them one of them (the necklace). I mean, you've got to love everything about them"
In one episode, Archie is busy with restaurant business to see Stephanie perform at a talent show. So Stephanie performs at the restaurant, making Archie regret missing it.
An early episode has Archie be friends with a former football player who is gay. It is charming that a show from the 70s has a homosexual come off as strong, charming, handsome and confidente and even Archie sort of accepts him in his own way.