In the episode where Adam and Jamie are making a "chicken gun", Jamie wants to use a piece of equipment that Adam is concerned would be too dangerous and risk blowing up, and Adam gets somewhat aggressive about it since Jamie just says he doesn't think it'll blow up. Jamie iterates to the camera that he doesn't hold Adam's concern against him, and later on when Adam learns of a safer and more fitting alternative, Jamie has no objections whatsoever to giving him the money and car to go buy it and is genuinely impressed with Adam's pick. Afterwards, Adam apologizes for his prior outburst, and the two go back to cracking jokes and working. The whole sequence of events is a great representation of how the two can work well together despite their spats and don't hold things against each other.
Adam getting violently and unexpectedly shocked thanks to Executive Meddling? Dude, Not Funny!. There's no footage of the aftermath, because the loyal cameramen and women insisted on giving him privacy—against said executive's orders. Coupled with Adam attributing this to them being a family thanks to all the time they've spent together over the years? Crowning Moment of Heartwarming.
After the death of often used EMS Paramedic Sanjay Singh, the episode "Storm Chasing Myths" featured a dedication of the episode, his last appearance on the show, in memoriam.
Erik Gates, the rocketry expert who regularly helped the team with myths since the pilot, received a similar dedication in "Mini Myth Mayhem" after his death in an unrelated construction accident.
Adam's former staff built an imitation astronaut suit for him. Now that's the sign of a staff that loves their boss.
Adam and Jamie's relationship is proof that you don't necessarily have to be best chums with each other to work well; the two do respect each other, and keep it professional and clean.
This extends to everyone on the crew. When Mythtern Christine was hit by molten sugar while testing Exploding Jawbreaker Jaime was always hovering in the background (he's waiting outside the bathroom door when she leaves, and can be heard just off-camera in the next cut) making sure she was alright.
In the Flights of Fantasy episode, the duo trained for a week to be passengers on a Lockheed U-2 reconnaissance plane going to the edge of Earth's atmosphere to see if it was the hardest plane to fly. (The myth was deemed plausible, but only because they didn't check on other planes.) There was only time and space for one of them to go on this once-in-a-lifetime experience... and Jamie ultimately deferred to Adam, admitting his conscience would not have been able to handle him getting in the way of his aviation and space nut of a partner. Adam's utter joy and appreciation for this in both his facial expressions and his comments (including a point-blank re-iteration to the camera that he owes Jamie one) are evident throughout and after the flight.
When Adam and Jamie visit the White House for the "President's Challenge" episode, President Obama praises the show and what he feels it's done for science education and popularity. There's a distinctly different quality in the President's voice tone between him giving the MythBusters their well-deserved praise and then falling back on script to talk about the myth setup. No doubt here that the President's sentiments were 100% genuine. He finishes and Jamie responds, "Well, thank you, sir", and you can hear Jamie holding back his emotions. This is James Franklin Hyneman, The Stoic if there ever was one, moved to tears.
In the cat myths episode, during Adam's attempt to herd cats, he eventually resorts to picking up the cats and dropping them into the pen. At one point, he picks up two cats and they lash out at each other. Adam immediately puts them down and apologizes to them, realizing that he should have known such an action would make the cats defensive.
The final episode:
When Adam is visibly crying before driving down memory lane you realize what the show means to him. The sheer size of the setup really drives home how much stuff the show has done over the years. And considering what ultimately happens to it, it's really a fitting tribute to the show's history.
In an odd way, Buster's last flight: Strapped to a rocket sled and vaporized against a stone wall. It's effectively the Mythbusters version of a Viking Funeral.
The reunion show, where Adam and Jamie get together with the build team to reminisce.
The messages from various famous fans of the show, including Stephen Colbert, James Cameron, Neil deGrasse Tyson, and even Barack Obama, all expressing their gratitude to the cast for creating a show that was both entertaining and got so many people interested in science. Obama's "thank you" near the end in particular can make even the viewer tear up.
Jamie reading a letter from a fan about how watching the show had inspired her to turn her life around and become the first person in her family to go to University. It says a lot that Jamie, usually The Stoic, starts choking up a bit as he reads the letter.
Perhaps the most emotional part of the special is a testimonial from a woman who managed to escape a sinking car (along with her daughter) thanks to seeing an episode about the best way to escape from a submerged car.
The cast members discussing which moments of the show they're most proud of.
In true Mythbusters fashion, Adam presents each member of the build team with a chunk of Buster's remains as a momento. It's a somewhat silly gesture, but all of them clearly appreciate the gift.