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.
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".
Lazar Wolf stopping by to say his farwells 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.
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.