Lister's attempts to get Kryten to break his programming. Lister, as a Working-Class Hero, despises the whole mechanoid slavery thing and the controls put upon droids by way of Robot Religion amongst other things. Lister not only sees Kryten as a sentient being, but as a friend and much of Kryten's Character Development is due to Lister's influence.
In "The End", Lister's actually touching response to Rimmer's existential crisis about being a simulation with his memories and thus not really "him"; pointing out that it doesn't matter and that while he might be dead, the fact they're talking proves he's still alive in some form and thus not truly dead in his opinion. Lister then proceeds to treat him exactly like he would have when he's alive, by immediately calling him a smeghead...
Lister would rather forfeit his entire wages and go into stasis for 18 months than turn over his pregnant cat and watch as it got destroyed for breaking the quarantine, ultimately spending 3 million years in stasis due to the drive-leak. The Cat's religion wasn't exactly wrong in their belief that "Cloister" sacrificed himself to be frozen in time, so that their entire race might be allowed to live.
A blink-and-you'll-miss it moment in the second episode; when Lister exclaims "Oh crap!" about Rimmer being the one brought back as a hologram to keep him sane, it ends up calling out a talking toilet. When Lister clarifies he didn't mean to call it, it says goodbye good-naturally and Lister even nods a goodbye in its direction. Goes to show that Lister really does treat anything with sentience with respect, even if it is a talking appliance.
In "Waiting for God", Lister — who has discovered that the race of Cat-people who evolved from his pet cat worshipped him as their God 'Cloister the Stupid', has discovered a dying, blind cat-priest who has lost his faith and succumbed to bitterness. Making a grand entrance as Cloister, Lister ensures that the man goes to his grave happy that his God has finally validated his faith:
Priest: (despairing) You tested me, Cloister, and I failed...
Lister: No, you didn't fail, old man. You passed. I'm giving you an A-plus Distinction.
Priest: You mean... there's a place for me on Fuchal?
Lister: A place? You got your own bathroom ensuite. Corked floors. Your own barbeque on the patio, double-glazing. A phone, everything.
Lister: No, you haven't! [Takes the hat off of Cat's head and puts it back on the priest]
Priest: A miracle! [begins to stand up] This is the happiest moment of my li-(dies).
The fact that despite how annoyingly selfish he is, Cat still visited the Priest often. Sure he was pretty clueless after the old man died, but it is Cat.
Also, the priest told Cat to burn his sacred hat, as a symbol of the lies. Cat just puts it on and lies that it's burned. Now why would he do that? Did he just want the hat for himself despite the fact that it looks silly, or did he genuinely have respect for the blind dying priest who raised him the best he could?
Rimmer also seems genuinely upset and frustrated that he can't help Lister himself, being a soft-light hologram at the time. He runs back and forth between Lister and Cat, almost pleading with the latter for help. He then spends the remainder of the episode telling Lister that he needs to get better.
It's brief, but in "Kryten", Kryten gives a description of a dream he has to Lister about a garden with growing plants. It's sort of cute.
Crossed with Tear Jerker in "Better Than Life", but the fact that Lister genuinely tries to comfort Rimmer after he learns of his father's death. It's the first time in the series that Lister has interacted with Rimmer as something other than an antagonist/annoyance, and shows that he really does care about his shipmate, however little he'd ever admit it.
In "Thanks for the Memory", the crew celebrate Rimmer's deathday. Afterwards, a drunken Rimmer tells Lister that he only ever made love once in his entire life. Lister decides to fix things, and adjusts Rimmer's hologrammatic memory...
Rimmer: You gave me eight months of your memory... as a present?
Rimmer may have been drunk out of his mind, but it doesn't make it any less heartwarming that he called Lister a decent person despite being made with the 'wrong ingredients", and fell asleep by singing a song he was saving for the girlfriend he never had.
Lister's absolute joy at seeing Petersen in "Stasis Leak".
The moment in "Timeslides" when Rimmer and his childhood self salute each other. Compared to any other time Rimmer encounters a duplicate of himself, it's pretty sweet.
When Rimmer first discovers a way to change history again. His first thought is that his actions will bring back Kryten and The Cat, he does care.
In "The Last Day", when Kryten is to be replaced by the latest android model Hudzen 10, the crew, hung-over as they are, vow to fight to protect Kryten. Even the normally selfish Cat. Kryten muses if this is the human quality called "Friendship". Lister says "Don't give me the Star Trek crap, it's too early in the morning!"
Also Kryten's entire "night to remember," if only because it's one of the rare times when all the Dwarfers are working toward one goal without bickering, something that's usually damn near impossible, in order to give Kryten a decent farewell.
Rimmer shows that he's surprisingly tolerant of Kryten's Robot Religion by stating that everyone is entitled to their beliefs, no matter how bogus. His own parents, incidentally, are Seventh Day Advent Hoppists due to a misprint in their copy of The Bible.
In "Justice" when Kryten calls up Lister as a witness in Rimmer's trial, one of Kryten's questions was "Who would you say, then, is the person who thinks of him most fondly?", to which Lister admits "I do." The computer could tell if he was lying. So deep down, Lister really does care about Rimmer* Although it was supposed to be a Stealth Insult; Lister is the person who thinks the most fondly of Rimmer and he just described Rimmer as a git, because nobody actually likes Rimmer.
Throughout "Dimension Jump", Ace puts up with all of Rimmer's insults. The only time he ever got genuinely angry was when Rimmer made a jab at Lister. Ace is pretty much the only person to put a genuine effort into liking Rimmer. It doesn't work, but it's the thought that counts.
Has to be said, though, that Ace's very first exchange with Rimmer ends with him mocking him for not having a plan. Given that, at this point, Ace knows nothing else about Rimmer, he's basically just having a dig at him for not being as awesome as he is.
In "Holoship", when Rimmer lists all the reasons he considers himself a failure, but Lister actually tells him there was nothing wrong with his job or the way he lived his life.
When Rimmer says goodbye to the rest of the crew, his speech is half-Heartwarming, half-Funny but the best moment comes afterwards. Lister says a quiet "see ya smeghead" and Rimmer actually gives a small smile.
Rimmer, the supposed ultimate self-centered Jerkass, finally proves he really is a Jerk with a Heart of Gold when he resigns his new commission on the Enlightenment in order to allow Nirvanah Crane, the officer who had fallen in love with him and sacrificed her place (and therefore her very existence) to let him live his dream life on the ship, to be reactivated and reinstated.
The rest of the crew might be faking their affection for Rimmer at the end of "Terrorform", but they certainly aren't faking the lengths they were willing to go to to rescue him from the Self-Loathing Monster's lair.
Kryten: Sir! Another barrage could bring down the ceiling and bury us all!
Rimmer: You'd risk your lives for me?
Kryten: Of course! You're part of the crew.
When Cat shows loyalty to Kryten over Rimmer in "Quarantine". A far cry from his attitude way back in "Backwards".
A small moment, but in "Back To Reality" Rimmer stumbles while getting out of the AR machine and Lister reaches out to steady him, even holding onto him while Rimmer regains his balance.
When Rimmer (drained of his bitterness and negativity) selflessly throws himself on the grenade in "Emohawk: Polymorph II". He survives the small explosion, but did so without knowing he would. Also counts as a Moment of Awesome.
At the beginning of "Out of Time", Rimmer gives the others an epic "Reason You Suck" Speech about how much they annoy him and how much he wants to inflict bodily harm on them. Then, in the closing moments of the episode, he witnesses them all being killed one by one by their own future selves, and he immediately becomes overcome with emotion before deciding to risk life and limb - and potentially time itself - to bring them back.
"Stoke Me A Clipper". There are quite a few little moments in this one, but the best is at the end, when the crew are having a funeral for "Rimmer" (actually Ace) and Lister awards him a posthumous First Officership. Then all the crew perform a Rimmer-salute.
Adding to this is what what he's awarded the officership for: succeeding in his mission to keep Lister sane. After dozens of episodes of them butting heads and insulting each other, it's clear that Lister does (granted, in an odd, twisted way) appreciate Rimmer.
Even better, when Rimmer leaves, he shakes hands with Kryten and Cat. But he and Lister hug. It's implied that Kryten and Cat genuinely believe that their Rimmer is the one who died but Lister is fully aware of the truth.
And the preceding space cemetery scene. The rings of a planet are made up of uncountable Ace light bees. Lister points out to an unconfident Rimmer that he's unlikely to break the chain. And the music is wondrous. It's an amazing scene, really.
Even more so when you notice that the ring of light bees resembles the ring in the show's logo.
After Rimmer rejects Ace's invitation for a chat, the others keep encouraging him to go talk with Ace. Until they finally stare at him relentlessly in order to guilt trip him. They're not doing it to bully him, they just want Rimmer and Ace to get along.
In general, the whole idea of the episode is one big heartwarming moment. For six series, Rimmer has been a self-hating loser who believes that he's a waste of space and ultimately will never accomplish anything. This episode is where he finally proves, to himself, Lister and the existence itself, that he's capable of making something of himself and making the multiverse a better place for his existence.
"Ouroboros" from the extended version, Lister and Kochanski's heart-to-heart talk about their unborn child. Kochanski asks Lister if he wants to pass on any advice about life to the child, and assures him that she'll tell the child all about him. Lister shares with her how he doesn't want the child to grow up feeling abandoned and rootless the way he did. It's all very honest and sweet until Kryten bursts in.
"Beyond a Joke", when Kryten realizes that he's been able to make something of himself and do so even though his jilted creator had invented him as a Take That! at her ex.
When Able accidentally gives away their location to the Simulant, and next thing they know he's flying away in one of Starbug's escape pods. Kryten thinks he's just saving is own skin...but then it turns out Able was just getting close enough to unleash all of his and Kryten's pent-up negative emotions on the Simulant, ultimately saving the others at the cost of his own life.
From "Nanarchy", the moment Lister finds the very familiar wristwatch device and buffs it's surface to reveal the very familiar image of the long absent Holly.
After the nanobots have restored Red Dwarf (sort of), we get to see the ship again after a more than two year absence. Best of all we get to see it like it was in the first series. Before the show runners switched over to the CGI model.
Hearing the series original opening theme play as Cat inspects the newly rebuilt Red Dwarf.
The moment from "Back in the Red" when Rimmer enters the bunkroom, Lister (now confined to quarters) is genuinely happy to see him. Subverted a second later when it's made painfully clear that this isn't the "grown up" Rimmer we've grown to respect over the past six series...
Lister: (Lister spots Rimmer walk in) Rimmer!
Rimmer: Word's out they're going to throw the book at you, Listy! Followed by the bookcase, and then the library, brick by brick.
In "Cassandra", when Lister, Cat, Kryten and Kochanski attempt to defy Cassandra's prediction of Rimmer's death by forming a 'protection circle' around him as they head back to the diving bell.
"Pete." Now, Pete had just been turned into a T-rex because of some unforeseen events. Take note of his behavior in part 1 after he's been turned into Barney's ugly brother: He does not attack the Dwarfers straight away. When Birdman stands up and sees him full, Pete doesn't attack him either, just... sneezes. It's not until Birdman offers some seed that he is eaten. In a way, Pete was still thinking like a sparrow. He just wanted some seeds to eat since it was offered and he was still tame. It wasn't until Birdman had been eaten that Pete found out that flesh was good to eat and then instincts took over.
The ending of "Only the Good...", Rimmer actually returns from the mirror universe, despite the fact that he has everything he's every wanted in life. He's the captain of Red Dwarf, he's respected among the crew, and the ship isn't falling apart. Despite all this, in the end he still goes back to "his" Red Dwarf.
Back To Earth
Lister meeting the two kid fans on the bus. It's adorable watching them reassure him that, despite all faults, he's heroic and cool to them. They also theorize Kochanski's not dead, turns out despite the fact that they were an illusion, they were right.
Every time Holly's mentioned, it's always in a positive way. Showing that all the crew, including Rimmer (in his twisted way) care for the senile AI.
Whilst it is played for laughs, Lister's video pep talk to himself in "Fathers and Suns" is essentially his rather bizarre way of acknowledging his shortcomings and attempting to better himself. Especially since it actually sticks. In subsequent episodes Lister is indeed seen studying for his robotics exams.
Small moment in "Lemons" - when Kryten talks himself up that he's "no longer the one dimensional cleaning droid (he) once was", Lister and Rimmer team up and torment him a little. It's so rare to see them in such perfect sync with each other, even if it is at Kryten's expense.
The revelation that Rimmer's mother gave him the middle name Judas because she was a member of the Church of Judas, which believed that Judas was actually the twin brother of Jesus Christ, who sacrificed his name and reputation to be crucified in his place, so he could help spread his brother's message of peace and compassion throughout the world, and she wanted her son to have those qualities. Made even more touching as the ending of the episode suggests that this belief was actually right.
In "The Beginning", Rimmer finds out that the man he thought was his father was not, and that his real father was in fact 'Dungo' the family gardener, causing Rimmer to be struck dumb. Despite being portrayed in typical Red Dwarf fashion, both Kryten and Lister appear to feel sorry and show concern for Rimmer:
Kryten: This is the worst thing that could happen: Mr. Rimmer has always had a hugo ego and no self-confidence.
Lister: Now his ego's smaller than a pixie's right nut after an icy bath. Well ya know, he thought he came from a military family -high flyers, success ingrained in the very core of their DNA- now he discovers he's no better than me.
And then upon Rimmer's return, he reflects that he no longer hears the voice of the man he thought was his father constantly demeaning him and destroying his self-worth, but that "Dungo.. Dennis.. Dad.." would be so proud of everything he'd accomplished in his life. After Rimmer's plan works and he gives the order to return to Red Dwarf, he proudly declares "The slime's coming home."
Which is a great Call-Back to the ending of the very first episode of the series, "The End".
In "Twentica", Rimmer points out that Lister can stay on the alternate Earth now that the Expanoids are going to be destroyed. Lister objects because Kryten would be killed as well. Kryten assures him that it's okay. Of course, once he finds out that he's going to be killed as well, Rimmer changes his tune to "LEG IT!!!!"
In "Give and Take", when Lister and the Cat are about to have their organs removed by Asclepius, Rimmer and Kryten enter. Without hesitation for his own life, Rimmer opens fire on the robot, Kryten then fires his bazookoid as well. These are two people who care a lot about their fellow crew members.
After damaging the robot; Rimmer and Kryten get Lister and the Cat back to Starbug, minutes before the station explodes. A brilliantly epic scene with an amazing score.
Rimmer giving Snacky a Dare to Be Badass speech, encouraging him to be more than just a snack dispenser.
In "Can of Worms", it may or may not have been part of a dream, but Lister coming into the Cat's room to reassure him that being a virgin doesn't mean he's a loser, and that he just hasn't found the right girl yet, is pretty sweet.
The huge audience reaction when Holly appears in "Skipper". On the making-of documentary on the DVD, Danny John-Jules says that he was several floors above the studio getting into the full-body Mr Rat costume, and the reaction was so enthusiastic he was still able to hear it.
The studio audience are audibly moved when they see the recreation of the Series I bunkroom.
The original model shots from Series I-V return in the final universe Rimmer visits.
Although it obviously doesn't last long, Rimmer finally manages to find a universe where he has everything he wanted: he's alive, an officer, married with four children, and Red Dwarf is about to arrive at Earth.
The Promised Land
Everyone is thrilled to get Holly back online. Even Rimmer is eager to get him back.
Even more so when they restore his original memories.
When Rimmer considers shutting himself down to conserve Starbug's power, having undergone a Heroic BSoD after The Cat points out that he's not really him, Lister talks him out of it. While it takes time, Lister eventually comes up with the analogy of sunlight reflected off the moon.
As an added bonus, the entire scene is shown with almost total seriousness. Lister sounds very stressed at the idea of Rimmer dying.
Lister also makes sure to look through the window of the cockpit door to make sure Rimmer started recharging again.
The Cat, when offered to join the Ferals by his brother, states that Red Dwarf is his home.
Kryten allows Rimmer to share his battery as they board the Dwarf, rather than making him drag out extension cables as they had on the Iron Star.
Although he drags his feet a little, Rimmer sacrifices his diamond-light drive to revive Kryten.
While Rimmer is in diamond-light mode during this scene, Lister has no problem using the "Mighty Light" nickname he'd given himself.
The Cat People start worshiping Rimmer, giving him a rare unambiguously happy ending to an episode.