In the Series 1 episode "Boston", when Martin, the neurotic, often insecure pilot, finally swallows his pride and actually asks Douglas, his co-pilot but also a former captain, for advice, suprisingly Douglas doesn't respond with his usual vitriol :
Douglas: Well, the main thing is, you've got to stop asking for advice. Martin: Great, thanks. Douglas: That's OK, you can start just as soon as I've given you mine. You're the captain, Martin. And one of the many excellent things about being captain, along with the irresistible sexual magnetism , and first crack at the cheese tray, is that you're always right. So by all means, take opinions, but remember, you don't have to listen to Carolyn, you don't have to listen to ATC, you don't even, and savour this, because I shall never say this again, you don't even have to listen to me. You're the boss. What you say goes.
Although she backs down quickly, Carolyn telling Hester MacCauley off for snapping at Arthur in "Cremona" is quite sweet, given how rare shows of affection - however subtle - are from her.
In the Series 1 episode "Fitton", Arthur is relating the things that make him happy, which are all rather simple pleasures - slipping into a warm bath, cracking your knuckles, etc. The only one Martin and Douglas agree with him on is the feeling of tossing an apple back and forth and hearing the noise it makes as it smacks into your palm. This leads to one of the shortest, sweetest moments of the series, as Douglas starts singing "We're Busy Doing Nothing", and the whole crew happily joins in.
In "Johannesburg," Arthur's repeated encouragement of Martin to take the lead away from Douglas's belittling comments — especially because it works.
In the Series 2 episode "Gdansk", Martin rants about how he's never won anything in his life. Rather than teasing him like usual, Douglas, after he hears the rant, decides instead to help Martin win a competition against Carolyn by giving him hints to the names of all of the Seven Dwarves. For Douglas, who usually takes great joy in seeing Martin upset, that is outright kind.
The entirety of the Series 2 Christmas special, "Moloka'i", starting from the pre-flight check reference to "The Night Before Christmas":
Douglas: Air con? Martin: Off. Douglas: Anti-collision light? Martin: On. Douglas: Fuel pump switches? Martin: On. Douglas: Dasher? Martin: On. Douglas: Dancer? Martin: On. Douglas: Prancer and Vixen? Martin: On. Comet? Douglas: On. Martin: Cupid! Douglas: On. Martin: Donner and Blitzen? Douglas: To the top of the porch, to the top of the wall. Martin: Dash away Ö Douglas and Martin: Ö dash away, dash away, all!
In "Rotterdam," Martin starts out incredibly jealous of the actor Carolyn hired to play the captain for the pre-flight film — conveniently also named Martin — who is taller, better looking, and looks better in a pilot's uniform. However, over the course of the episode, he discovers that he and the actor actually have an awful lot in common; as the actor too lives for his passion (acting) but not getting any recognition for it and not being able to live off it. In the end, the two Martins hit it off and become friends, agreeing to go out for a beer when they get back home to Fitton.
Following the Douglas-being-nice-to-Martin trend, here's a small cut scene from Series 3's "St Petersburg" (from John Finnemore's blog):
Gordon: Just got in. Bloody hell, the crosswind, eh? Hairiest landing Iíve had for years! Martin: Yeah! You should try doing it on one engine! Gordon: Jeez, I wouldnít want to! Did you? Martin: No, I didnít! Gordon: Oh. Right, I was gonna say! Martin: No, I mean, I didnít want to either. Douglas: ...However, he absolutely did. Rather well, actually.
While the crew's plan to freeze Gordon's hands to the plane console was partially so they could get GERTI back, it's clear that they were also taking a wicked glee in shaming Gordon for his horrible treatment of Arthur involving the gin bottle present. It's rather sweet hearing them all come to Arthur's defense indirectly.
During Series 4, Carolyn repeatedly tells Martin to look for other jobs so that he can earn a respectable salary, as she's sick of not being able to pay him. It's sweet to see that Carolyn really does care about Martin, but when you consider that MJN would almost certainly go bust without him, it appears that she's actually putting Martin's happiness ahead of her own business.
Also consider that Carolyn is torn between staying in Fitton for MJN, and moving to Switzerland with Herc. If she could no longer sustain MJN, the decision would be much easier for her. Effectively, she's urging Martin to move on as a roundabout, possibly subconscious way of getting herself to move on so she can be with Herc.
In "Xinzhou," the crew keeps having to get up every twenty minutes to clear snow out from the intake despite the fact that they all need rest. In a sweet (though, of course, shortsighted) thought, when it's Arthur's turn, he tries to take it upon himself to stay out in the cold to keep the intake clear so that everyone else can sleep.
A real life example. During a recording for the fourth season, John got a very special surprise. In between seasons his fans on Tumblr had been taking pictures of the traveling lemon at various landmarks all over the world, and they decided to make a book out of it. One of those fans presented it to him personally, to his absolute glee.
The joy on his face upon receiving the book is absolutely heart melting, as is his words of thanks to the fans.
When Martin manages to get a date from the Princess of Lichtenstein, Douglas' reaction is to be genuinely pleased for him (and impressed).
In "Yverdon-les-Bains," Martin learning of the crew's high praise for him when the results of his co-worker evaluations come back: Carolyn and Douglas both rate him highly as a pilot (Douglas, as usual, in a typical Deadpan Snarker fashion), and Arthur describing everything he does, on a scale from "poor" to "very good," as "brilliant!"
In a small way, Douglas's indignation when Arthur calls Herc "Skip."
Douglas: Heís not ĎSkipí. Martin is Skip.
MJN flying out to pick Martin up from his interview.
Firmly establishes that Martin and Princess Theresa are now in a relationship and are very happy together.
Martin ending up in Swiss Airways as a First Officer, sounding absolutely professional and dignified, just like he'd always dreamed of.
Carolyn finally says "I love you" to Herc in Zurich.
Herc choosing to stay in England and fly MJN with Douglas in order to stay with Carolyn because he loves her that much. Aww.
...But Douglas will be Captain.
Carolyn changes MJN to OJS, "Our Jet Still" Air, signifying how GERTI now belongs to them all, having been with them through thick and thin.
The fact that the series ended with a very loud, very enthusiastic "BRILLIANT!" from Arthur.
Meta: It was well-known in the fandom that John Finnemore's dad acted as unofficial aviation advisor for the show, checking over the scripts for accuracy, and many fans on social media noted how heartwarming it was to hear him finally credited at the end of the show.
From John Finnemore's blog, regarding Arthur's "test" for Zurich. Aw.
Arthurís test was to stand up to the false (if biological) father in his life, firstly at the auction and secondly and most importantly by remembering his grandmotherís name, realising that he will never, ever have a genuine father/son conversation with Gordon Shappey; and renouncing him once and for all in favour of the two genuine father figures in his life Ė and in particular, the one who has always looked out for and defended him, even as he mocks him; the one with whom he can discuss the dames and the horses over a few pineapple juices; and the one on whom he can utterly rely to do something clever, and make everything alright.