"Funny Aneurysm" Moment: Remus teases Sirius about his seeing "draperies" in his crystal ball during divination class and jokes about his friend's future in bridal couture, to which Sirius corrects him by saying they're actually veils.
Sirius jokingly remarks that Remus will outlive all of the Marauders.
From the Halloween installment: Remus is "well aware that he is the sidekick with the books who hangs about in the back being a good influence with a posh accent and then is killed tragically just before the climax." Written years before the last book came out, no less.
"Anyway, he can't work a defensive spell if his life depended on it, which it would. You know how he gets when his blood's up, all laughing and insane and hopping about talking nonsense and all of a sudden someone would hit him in the chest with a hex before the possibility even occurred to him." - From Part 25, from James about Sirius as to why Sirius shouldn't fight Death Eaters alone. Also counts as a Tear Jerker.
At one point, Peter notes that Sirius would get him killed.
After the death of James' parents Lily quietly asks how long it will be until it's one of them that gets killed.
Growing the Beard: around the time of Part Twenty-Two, the series, though still side-splittingly funny and romantic, takes a much more serious tone, especially when dealing with Voldemort's rise and the death of James' parents
Ho Yay: James and Sirius' hero-worship of the Prewett Brothers reeks of this, to the extent that Sirius seriously considered wearing a pink shirt reading 'Mrs. Fabian Prewett' in public.
Also, the spells Dumbledore casts in part 16 to make the school act out a horror movie invokes this in the Slytherin girls.
And Sirius and Remus are very touchy-feely before it becomes clear that they're an item.
Also, the talk between James and Lily when James returns from his Auror training, after having been ambushed by Death Eaters and saved by Sirius. It's all at once funny and so, so heart-rending, mostly in the way that Jaida and Rave manage to flawlessly capture the amount of pure love Lily has for James and the terror that that love inspires, and in such realistic terms.
"No," Lily snaps. "We can't just, we can't just anything. I know I only have a stupid desk job, James, but I've seen what the Death Eaters can do – what they have done already! – to people. I don't want you brought in there like that. James, I love you, do you have any idea what it means?"
"Yes," James tells her. "Actually, yes, I know exactly—"
"You do not!" Lily's voice tears off, sudden and awful to hear. "It means that I'm terrified, I'm terrified all the time, and then when they brought Sirius in and you weren't there, what was I supposed to think?"
"That I was making my report," James says, mouth dry. "That I was telling Dumbledore what happened."
"That you were in seven hundred pieces somewhere. Gone. Forever." Lily stares at the ceiling, clenching her own forearm so tightly that James wants to take her hands before her nails reach bone.
Realizing that ever single named character except for Professor Mcgonagall and Kingsley Shacklebolt was killed or had their lives otherwise destroyed by the Death Eaters. And there are quite a lot of named characters.