One Time Lord. One Great Detective. Two obsessed fanfiction writers…
There are things called Fixed Points in Time. They're events—births, deaths, decisions—that must always happen. They must always happen, no matter what... or Time will start to fold in on itself. Things like the signing of the Magna Carta, or Columbus's discovery of the New World... Or a certain meeting at St. Bart's, in 1881.
Aerith and Bob: Sherlock and Beth, and then their surnames make a flip: Holmes and Lestrade.
Animal Motifs: Used sometimes in-universe. Holmes is described as alternately aquiline and feline (as per Canon), Ten's Puppy Eyes get mentioned a fair bit, Moriarty retains his serpentine qualities, and Moran is as much the tiger as ever.
Emotional Torque: The series as a whole, the first season's finale as a trilogy, each episode of the finale themselves, and the first episode of the second season.
Fairy Tale Motifs: All over the place, and rightly so, considering that the love stories especially read like dressed-up fairytales with time travel.
The final episode of the first season plays this trope quite blatantly with the title "Every Good Fairytale".
One extracanonical idea of one of the authors has Katherine Watson traveling far back in human history and telling people the stories of her parents and her godparents in a way that they will understand, making those love stories the Ur Example for fairytales.
Only a Flesh Wound: Regularly averted. If a character is shot, he/she is screwed. (The fact that one may have Time Lords or TARDI Ses nearby does not negate the severity of the gunshot wound — a victim might be healed quickly, but they will still be realistically injured, first.)
Dr. Kit Bennett has no problems in shielding a trio of civilians on a top-secret military base and investigating disappearances with them.
Beth appears at first to have been inspired in her rebellious tendencies by Holmes, but meeting her father makes it clear that the original Inspector Lestrade's strict adherence to rules faded out of the gene pool somewhere along the line.
Wham Episode: "Child of Time", wham. A teenage Beth Lestrade from Sherlock Holmes in the 22nd Century makes her debut and makes the series a three-way crossover. "Watson and Sparrow", wham. Sally Sparrow is about to become the mysterious second Mrs. Watson. "Dynamics of a Point", wham. Holmes and Watson have a terrible break-up, Holmes is quite visibly darker, and Moriarty is Back from the Dead. "The Dying Detective", wham. Holmes manages to make himself just about as soulless as Moriarty ever was, and Beth is killed. ...it would almost be easier to give examples of episodes that don't deliver a wham.
The X of Y: Children of Time, "Men of England", "Child of Time", "Dynamics of a Point".
British Accents: Comes up every now and then. Holmes and Watson, of course, speak have pre-BBC, pre-20th century accents, which becomes important for Beth when she's working out who they are. Beth herself can speak a decent Cockney; her family spends summers in the UK, so she's gotten the hang of that particular accent without losing her own Midwestern one. The Doctor's own Estuary accent is mentioned early on in Holmes's thoughts. Kit deliberately switches from a Midwestern accent to a middle-class London one in 1940s New Mexico.
Broken Bird: Kit in spades by the end of "Manhattan". Beth, mid-"Every Good Fairytale".
The Other Darrin: The two authors switch back and forth in writing Watson, depending on if he's alone with Holmes or if they're with the Doctor, etc. Other characters also get switched around, primarily for the finale.
Broken Bird: Beth is definitely this at the start of the season, and if Season 1 could be said to be ultimately about Sherlock's Character Development, Season 2 might well be ultimately about hers. Initially after Sherlock's rejuvenation, she seems okay, but future episodes prove that she's very much not to the point where even Professor Moriarty remains concerned about her.
Daddy's Girl: Beth as noted by several people, her boss included.
Good Is Not Nice: NSY and cryptnosis. To be fair, not all Yarders are jerks like Chief Inspector Grayson.
Iconic Outfit: Beth kind of likes the deerstalker-and-Inverness look, and insists that the Inverness, at least, should be kept for familiarity purposes.
Insatiable Newlyweds: Still sort-of newlyweds and having been parted for so long... the Holmeses get very romantic very often.
Large Ham: Moriarty carries definite shades of this, certainly enjoying messing around with the heroes.
Late Arrival Spoiler: The entire first episode, due to being a direct continuation from the previous one. If you haven't read the season 1 finale episodes beforehand, "Renascence" will quickly give away the majority of it all.
Historical Hero Upgrade: Right after this trope has been applied to Tesla and Westinghouse, Bram Stoker gets in on the action... in Paris, of all places!
Lighter and Fluffier: On the whole. They definitely start out on a light note with a tour of the TARDIS, but the second TARDISode plunges right into good ole gut-wrenching angst.
Noodle Incident: What happened when the Doctor & Co attended a cinema event in Paris is never actually shown (taking place between "The Icarus Experiment" and "A Study in White"), but much discussed later on.
Ship Tease: The pre-finale TARDISode for Season 1 has Holmes giving Beth a tour the best he can... with alternating moments of awkwardness and cuteness.
Team Mom: The TARDIS never rests, watching over her boys...