Serenity/Heartwarming

For many viewers, the entire opening with River's rescue finally recounted takes the cake.
By the end of the film, Jayne has a measure of respect for Simon, and even offers a drink.
The rebuilding of Serenity in the end. Even Inara does her part.
The first 40 minutes pretty much confirm that Mal for one still doesn't trust River 100%. At the end of the movie... he's letting her drive.
It says a lot that the movie itself could be considered a meta-example. After responding to the fan petition, Joss Whedon started seeking out a way to make this movie, and Alan Tudyk decided to return a prop he reportedly filched off the Firefly set - the Big Red Button used in "Out of Gas", with a note quoting that ep: "when your miracle gets here, hit this button."
It's easy to miss, but while Serenity is plummeting toward Mr. Universe's planet, Jayne is checking the passengers' seat belts before he gets a chance to strap himself in.
- Including River's! I'm not sure about Simon's, but I do recall seeing him passing by River's belt to make sure it was done in. And if I recall, either River or Inara (I forget who) calls out for Jayne when he starts getting thrown around in the room when the ship is spinning out of control. Neither one of them had any reason to like him whatsoever, but yet they still care about each other when it counts.
Jayne saying "She's Right!" after Zoe tells him to stop after he says that River is "damaging his calm". Wait, did Jayne just agree with River?
Jayne saying these words: "Shepherd Book always said, 'If you can't do sumthin' smart, do sumthin' right.'" This is made even more poignant by the fact that before, he was criticizing Mal for going this route.
The final scene with Mal and River flying, when River asks him to say the words she knows anyway:

Mal: Love. You can learn all the math in the 'verse... but you take a boat in the air that you don't love... she'll shake you off just as sure as the turn of the worlds. Love keeps her in the air when she ought to fall down... tells you she's hurting before she keels. Makes her a home.

- Mal calling River a "little albatross".
Let's not forget how River's Crowning Moment of Awesome - taking on an entire room full of Reavers and winning - was born of a desire to protect her brother and friends the way they've protected her.

"No. You take care of me, Simon. You've always taken care of me. My turn."

The last minute or so. The music, the visuals, the audience, and this:

River: Storm's getting worse.
Mal: We'll pass through it soon enough.

- And they do. Both literally and metaphorically.
- Special points to the ship flying away. The image of a multi-ton replica of a crippled bird in cast iron, a thing that doesn't look like it should ever be able to fly, that crashed, not only achieving flight, but apparently punching physics in the face while doing so. It has done the impossible, and that makes it beautiful.

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