For the Doctor, this 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...”
The mere appearance, let alone involvement, of Jeremy Brett makes this episode an emotional one for Granada fans.
Holmes and Watson drift away further and further from each other, and it's really quite painful to watch.
Dynamics of a Point
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."
The Dying Detective
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.
Every Good Fairytale
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.