No spoilers. I haven't gotten to watch any part of the new episodes early nor have I read any leaked plot details. All the following is just guesswork on what I expect to happen and, in part, what I want to happen for Season 4.
My cred so far: before we ever met the show's Mary, I guessed she'd be the first of Watson's ladyfriends known to actually like Sherlock. I was right! Maybe I will be again, or maybe I'll have to eat any number of the words below.
Anyway, let's start there.
About Mary
In case there's any doubt, I think Watson really did throw the memory stick marked AGRA into the fire without reading its contents. But it would make all the sense in the world if he had Sherlock look it over first and even memorize it. Sherlock could disregard any feelings he may form on Mary's past. He could also be relied on to never reveal any part of it to John unless he judged there was a need to.
One of the forthcoming three episodes, I predict, will feature another milestone marker for the Watson marriage; maybe a baby shower, maybe a vow renewal ceremony. Some detail we barely notice will freak her out in the middle of the party and she'll vanish like she's the subject of a magic trick.
Sherlock will figure out where she went and go talk to her. She'll be considering leaving John without an explanation. Sherlock will talk her in to returning long enough to reveal where she's going.
Mary will reluctantly come back to the party venue. She'll then introduce John to an American man and explain that he and she were undercover as a married couple on some long-term sleeper assignment. Mary will have thought her obligations were over, possibly because she thought her fake spy husband was dead. He, otoh, thought it was time to wake up the sleeper because duty calls.
Mary will have no choice but to resume her dangerous espionage career and leave John with nothing to remember her by except for their baby. For humorous purposes, Sherlock will suggest they rededicate the soiree as a going-away party for the two spies. John will react bitterly to Sherlock thinking he can celebrate the occasion.
Addressing alternative fan theories: one suggestion that's been circulated on the net is that Mary (maiden name: Morstan) is doubling as the show's counterpart for the literary Colonel Moran. I can't fault this as a possibility but I personally hope it proves to be wrong. Making different characters into the same character is a form of fictional universe incest.
Since I've addressed one of Moriarty's lieutenants, let's now move on to...
The Fate of Jim Moriarty
This is the big one, right? I hope he really is dead.
That, of course, is where Sherlock would disapprove of my thinking. Theories formed first causes one to adjust facts to fit such theories instead of theories to fit facts.
But I still hope he's dead. It's canon, his nihilistic outlook on life is a great character beat, and it all makes for one less faked death on a series that's in danger of having too many.
There's also Sherlock's own statement on the matter: "He's most certainly dead. More importantly, I know what he's going to do next!"
But did Jim die on that rooftop? Sherlock implied that the old case of Amelia Ricoletti, the Abominable Bride, has plenty of bearing on the matter.
Also consider S3E1. When Lestrade calls "bollocks" on Anderson's bungee cord theory, one detail he DOESN'T ridicule is that the fake Sherlock corpse is actually Moriarty with a mask on. Later, in the Bride special ep, Sherlock is pretty clear that the corpse isn't Moriarty.
Deduction: neither Sherlock nor Scotland Yard know where Moriarty's remains are!
There's also a fairly compelling video essay on YouTube about Jim's death. It first replays Moriarty's crown jewel heist in which he sprays one guard with knockout gas. Later, when he shakes Sherlock's hand and draws his firearm, the exact same sound effect plays a second before he pulls the trigger. This implies it's a trick gun and he merely knocked himself out.
If there were more time, I'd go back and look for signs that Moriarty had a terminal condition. If his method really paralleled the Bride's, he could have simply gotten up after Sherlock's jump and lived out his final days in seclusion, shooting videos of himself and manufacturing other ways to fool the public into thinking he lived on. Worthy crime cartels could use his likeness to make people think he masterminded their wrongdoing.
Redbeard and the Other Brother
Canon significance: where'd this whole other brother thing come from originally?
As I understand it, it's specified somewhere in the Holmes stories that Mycroft and Sherlock are "country squires." And there's an apparently unbreakable tradition that the firstborn son will stay home and manage the family's property. Mycroft doesn't live in the country and that's the only reason people think there must be an older brother who does.
On the show: In S3E3, Mycroft mentions "You know what happened to the other one" in a context that strongly implies he's talking brothers.
Could the man in the promos who speaks of "endless fun" with Sherlock be the secret eldest Holmes boy? Idk. Doesn't look like he was cast for family resemblance. Anyway, there was something from the creators where they agreed with fans that it would just be amazing if they could get Tom Hiddleston (Loki in the Thor movies) to play him.
And I think the history and significance of Redbeard, the red spaniel, is pretty straightforward. Sherlock loved the dog as a boy and was heartbroken when the family had to put him down. It was an early lesson in emotional detachment.
However...
Addressing Alternative Fan Theories: another outlook I've read is more complex. In the Baskerville Hounds episode, Henry Baker's mental image of a scary dog is proven to be a reformed memory of a man he once saw. Some believe Sherlock has done the same thing, repressing some sad story about a lost brother and convincing himself the brother was just a pet.
If true, it's contrived contrived contrived. Why would Sherlock and Henry just happen to have the same bizarre memory quirk?
That's all for now! Time will tell how close to the mark I am. I'll go into more about how I came up with the Mary theory some other time.