On the alien planet, in a blink and you'll miss it moment, Jason shows that yes, he DOES know Guy's last name.
At the end of the film, the team has had a Dynamic Entry into the side of a convention centre, with Sarris dead and the fans ecstatic. Jason goes forward to bow, but then remembers that his team are there and tells them to all come forth, as he feels that they equally deserve the applause. They gladly accept, at which point Jason kisses Gwen. Contrast to the beginning of the film, when they were almost all reluctant to be there, Jason was hogging the limelight and Gwen couldn't stand him at all.
And as a metatextual heartwarming moment, we have Tim Allen, Alan Rickman, Sigourney Weaver, Tony Shalhoub, Sam Rockwell, and Missi Pyle (Laliari), taking their bows, which is something film actors rarely get the opportunity to do on-screen.
Brandon and his friends, and the way the movie treats them. These aren't useless, pathetic geeks wasting their lives in a juvenile fantasy; they're intelligent people with strong interpersonal friendships, who have an incredible amount of passion for a show that has been empirically proven to change lives and make people (aliens, in this case) believe in friendship, loyalty, courage, and a better future. It's a love letter to Trekkies and their devotion to the show. Hell, at one point, the fans save the day. And they save it solely because instead of just shrugging the whole thing off as just a stupid TV show, they connected with it on a deeply emotional level and created something wonderful.
On a meta level, the exchange between Brandon and Jason just adds to this—because while the events portrayed in the show obviously didn't really happen, the themes and the emotion that went into it were real.
Brandon: "I'm not some kind of brain case, okay? Of course I understand that it's all just a TV show, there's no ship—"
Jason: Brandon. Brandon! It's all real.
Brandon: Oh my God I knew it. I KNEW IT!
One for the con scenes, take a good look at the crowds in each of the cons. The con has people of all walks of life there: Men, women, children, married people, single couples, cosplayers, and so many more. It would've been so easy to show the fans as a bunch of overweight, under-washed neckbeards, but they didn't. They instead showed the truth, that fans come in all shapes and sizes.
One of the reasons Patrick Stewart, before finding out it was an Affectionate Parody, didn't want to see the movie was because he thought it would mock Star Trek fans.
When Jonathan Frakes finally convinced him to go see it, Stewart said that "no one laughed louder or longer in the cinema than I did."
Jason experienced a sad, in-universe Creator Breakdown in the beginning of the movie, in which he angrily admits to Brandon that Galaxy Quest is a dumb television show, nothing more, nothing less. And then, just as Jason drunkenly prepares for the inevitability of the dull reality of his fandom and the fact he's a shadow of his once truly successful acting self (while probably thinking I Wish It Were Real), Jason's faith in Galaxy Quest and his role's recognition gets restored more then ever. He gets to experience the real thing, created by an alien species, and despite being initially freaked out, he becomes genuinely excitable like a little kid whose imagination turns into reality. Seriously, watch Jason blabbering to the other cast members about the ship. He's so damn thrilled experiencing the fiction becoming real, and getting to play his role again in a real space adventure.
Despite starting out an egomaniac, Jason gets a Pet the Dog moment when he immediately decides to share his experience with his resentful co-stars, including an especially bitter Alexander Dane, in order to restore their faith in Galaxy Quest as well. Sure, they think he's full of it (especially after he lost some evidence to Brandon by mistake), but once they finally manage to get on the ship, they're awestruck. (Well, except Fred.)
Not to mention that later on, in Gwen's phone call to Alexander, it's implied that Jason NEVER mistreats a fan and appreciates them greatly.
It's also implied while the crew is arguing on the mining planet that Jason and Gwen had dated in the past.
Earlier while trying to explain to the Thermians that Galaxy Quest is just a show, despite their resentment of their fandom that they grew over the years, especially Alexander, they tried to break it down to them gently without any mean-spiritness or being so flippant that should be expected from actors who disliked being remembered for a certain show. Even when Sarris held them and Mathesar captive during their Darkest Hour, Jason became the most reluctant to break it down to the usually happy-go-lucky Mathesar, who then goes into a Heroic B.S.O.D. when realizing it.
Nesmith's farewell to Mathesar:
Mathesar: We were hoping you could come with us. Our people have no commander. Nesmith: Mathesar, I think your people have a great commander, sir. (salutes him)