For the Doctor, "Smith and Holmes" is right after "Doomsday" and "Christmas Bride". This episode might not be the thing to read if you've just watched those episodes...
The Doctor's It's All My Fault/My God, What Have I Done? moment. Especially when he starts breaking down into tears, although perhaps the moment that hurts the most comes when he's falling asleep and is afraid to.
Holmes: “And when was the last time you slept, Doctor?”
Doctor: “Dunno. Not in a long time... not sure how long... The screams usually wake me up again, anyway...”
Holmes's reaction to having to kill the zombie soldiers. As one of the authors pointed out (the one who writes him in the series)... unlike Watson, Holmes is not a soldier. His job is to find out who put the bodies there and how, not putting the bodies there in the first place. He breaks down into Heroic BSOD.
As does the Doctor when the sight puts him in mind of the Time War.
Let's talk about Kit for a moment. Kit is working on one of the most infamous military projects in history even though it goes against her beliefs, and she has to endure initial revulsion because of it from a man who's obviously like a father to her. She has to work with the Doctor, Holmes, and Watson, knowing all of them but without any of them knowing her. She's helpless to save a friend she promised to save (watching him die before her eyes, and for her sake, to boot), and her sacrifice is rewarded with torture that would likely have gone on until something gave in her link with the Time Vortex. (And that could have taken a very long time, during which she would have been constantly dying and being healed at the same time.) She couldn't save a man she'd come to respect, and then she had to watch the three most important men in her life leave, knowing where they were headed and unable to properly warn them or tell them who she was... And knowing that she would probably not see Watson and Holmes again, as they were already dead by 1945.
What happens at the end just makes it that much more heartbreaking.
And, of course, it doesn't help that Beth tells Holmes, early on, that Jeremy will be dead in six years.
Holmes starts the episode out with a chip on his shoulder, and it grows to monumental proportions throughout the episode. It's really painful to watch, and the crowning moment of the heartbreak is when he threatens to commit Heroic Suicide and there's nothing actually heroic about it — he's entirely willing to shoot himself because he no longer has much of a reason to live.
The break-up between Holmes and Watson. It is bad. It's all the hurtful things Holmes could ever say to Watson, and Watson's weariness of having to put up with it.
Holmes: This is, after all, the second time you have tied yourself to a young lady almost half your age, less than a fortnight after your first encounter. A pattern seems to be forming...
Watson: (gapes) I fell in love, Holmes! That does actually happen to people... Well, most people!
Holmes: Of which I am one of the notable exceptions – is that what you were subtly attempting to imply? My thanks, Doctor; you could not have paid me a greater compliment!
And everything is made worse by the "Always 1895" Motif.
Holmes's treatment of Beth quickly spirals into uncomfortable-to-read, as he really starts to act more like an Abusive Parent than The Mentor Beth has been trying to get him to be. (This, naturally, Foreshadowsthe choiceshe's about to make.) She finally calls him out on this by saying that he's "trying to control her, and he can't."
Holmes and Watson's final conversation with each other. The entire thing is painful to read, but it's the closing lines that get to you:
Watson: The sooner you stop caring, the sooner you'll be free of me and any stain upon your conscience.
Holmes: As you wish... Goodbye, Doctor Watson.
Watson: ... Don't let Beth die. Save, at least, a piece of your soul for her sake.
Holmes: As you said, Doctor, my soul now belongs to the Devil — you shall have to make the request of its new owner.
Watson's alternating anger and despair throughout the whole thing, locked away and entirely unable to stop his dearest friend from turning into a monster.
Sally and Beth, both brave, strong women, having to hold their own against a Crapsack World, on the run from Colonel Moran, and desperately needing the men they love. Beth wants Holmes back even though she's thoroughly convinced he'll never return her affection, and Sally craves the support of her husband, going through her first pregnancy and delivery without him.
Beth's attempted rescue and subsequent Heroic Sacrifice. Seriously, just try to get through the whole thing without at least wanting to cry.
Holmes: That is the very point which I have been attempting to make, my dear Miss Lestrade: that Sherlock Holmes is no more.
Beth: No. He can’t be. Because I need him. And the world needs him. And... and... I need him...
Holmes: Then I suggest you relay your message to his shade, wherever it may roam, and cease to bore me with your melodramatic sentiments.
Let's talk about Beth for a moment. She was already established as The Woobie by the end of "Dynamics", a role further intensified by "Dying Detective", and even though she comes back to life, she quickly descends into Broken Bird status, traumatized by the memory of her death and the memory of Holmes being, for all intents and purposes, Moriarty. All she can do is curl up on the floor against Holmes's chair, afraid of him but unable to leave him.
Even on the honeymoon, Sherlock and Beth can't stop dwelling on the past and the future. They try to avoid it as much as possible, but when they can't, the situation quickly spirals down into Inelegant Blubbering. For both of them. Sherlock's Face-Heel Turn haunts them both, and the thought that they might never see each other again downright terrifies them. The latter is made worse by the fact that they've both been through more than enough, and their separation is very much Yanking the Dog's Chain.