The song "Do You Love Me?" Tevye and Golde have been in an arranged marriage for twenty-five years, they've got five kids, and this is the first time the idea of love has even come into the equation. They quarrel and Golde ducks the issue, before admitting that she does. It doesn't really change anything, but, as they both say: it's nice to know. Awwww.
Motel singing "Miracle of Miracles" to Tzeitel.
Motel: But of all God's miracles large and small
The most miraculous one of all
Is the one I thought could never be:
God has given you to me!
The film version absolutely makes this song. Rosalind Harris, playing Tzeitel, doesn't have a word of dialogue the entire scene. And yet, while Motel is dancing around the forest like a giddy goofball, she never takes her eyes off him, and she's beaming the entire time. It's plain to anyone's eyes that she's bubbling up with just as much joy as her fiance - she looks like she's drunk on him, like her entire existence revolves around him, like she couldn't possibly ever be any happier than she is right at that very moment. It feels like the joy blazing between them should have burned the entire forest to the ground. This, tropers, is how a Heartwarming Moment is done.
Tevye's internal monologue about possibly letting Tzeitel marry Motel. He's made his bargain with Lazar Wolf, and believes that he's doing what's best for his daughter's future. But then he realizes, more important than money and security, is the fact that the two are in love. When he comes back to reality, he sighs and asks, "So children...when shall we have the wedding?"
Just look at my daughter's eyes/she loves him/she wants him...
When the Russians join in the celebration of Lazar Wolf getting engaged to Tzeitel. For these people, religion matters not.
This troper didn't see it as a heartwarming moment, but rather a tension filled moment.
There's definitely some tension, but once Tevye shakes the Russian man's hand and begins to learn the Russian dance the tension eases.
It's heartwarming because it shows that if not for the political pressures it would be possible for them to become friends. It's the possiblity of something better.
The song "Sunrise, Sunset".
Pay close attention to Tzeitel and Motel's faces during the scene where Motel puts the ring on her finger. That is the look of pure adoration and love and they're finally getting married.
Lazar Wolf stopping by to say his farewells to Tevye. He didn't have to do it but it shows a certain level of forgiveness on his part. Also, he wants to be close to Tevye even if he didn't end up marrying into Tevye's family.
It's especially powerful in the film, as after the two men say their formal (but still warm) goodbyes, they start to walk away...only to go back, throw their arms around each other, and hug tightly, implying that the feud is completely forgiven.
In the final scene, after Tevye's disowned Chava and acts as though she is dead and her pleas for him to accept her marriage fail, he finally cracks and lets out a quiet "God be with you" before she departs.
And in the film, he lets his wife tell her where they're going, so, maybe, they could someday talk again.
A meta example, but this troper got to see Topol, who portrayed Tevye on West End and in film versions, onstage during his "farewell tour," when he played Tevye one last time. He was well into his seventies, but seeing him bring such energy to the performance was a CMOH all on its own.
At the end of the Rich Man song, after painting a tale of grandeur and excess, Tevye says that the greatest thing of all about being rich, was the chance to sit with scholars and talk about The Good Book seven hours a day.
Also that bit about how his wife would be fat, happy, strutting like a peacock, and being able to order people around in the kitchen rather than slaving over the cooking herself. Just something very sweet about that.
When Tevye comes home for the Sabbath and starts kissing his daughters, one by one, proclaiming "This is mine!".
Very subtle, but following the curtain call for the latest revival, the cast breaks into a spirited dance as the curtain falls. Among those dancing is the Fiddler himself, showing that after spending most of the play only observing the action, he can now join dancing with the rest of the villagers.
When Tevye and his family are about to leave Anatevka forever, Tevye sees the Fiddler nearby, waiting for an invitation. In most productions, and in the film, Tevye motions for him to come along, implying that even though the community has been uprooted, their traditions will continue to travel with them.