These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Anti-Climax Boss: Moriarty. After being built for half a season, her capture in the Season One Finale was this for some..
Ass Pull: In "The Marchioness", the revelation that Joan slept with Mycroft during the events of "Step Nine" makes absolutely no sense within the narrative and pissed off the majority of the fanbase.
Broken Base: Female Moriarty was one thing. Having her and Irene Adler being one and the same was another. Her being in love with Holmes was the straw that broke the fandom camel's back.
Conflict Ball: One of the major problems of Season 2, so far. To create conflict between Holmes and Watson, the writers crafted ridiculous plotlines using Retcon, ignoring the evolution of the characters in the previous season and using sex as a plot generator.
Dolled-Up Installment: Many of the fan arguments surrounding the show boil down to defending the show on its own merits vs. attacking it as a poor adaptation of the original canon. One wonders if it might have been better received by purists if it had remained the same except under an original name.note Of course, we already have House...
Watson, despite being the Deuteragonist of the show, is by far the favorite character of the whole fanbase.
Alfredo and Bell have their fair share of admirers.
Ms. Hudson and Clyde the tortoise are also rather popular as well.
Ms. Hudson's popularity as both a Canon character and a positive example of a trans person could be expected. But after her debut episode, there's also clamoring for seeing more of another character appearing in the same episode: the crusty snow-plow driver, Pam.
Foe Yay: Between Moriarty and Joan, especially during the restaurant scene. Also, the traditional Holmes-Moriarty Foe Yay is given a new dimension by having Moriarty be a woman and having her and Holmes actually having been lovers once.
Fridge Brilliance: The bust that is smashed in the opening sequence is female, and has a haircut that strongly resembles Moriarty's in "Heroine".
Seems to be striking up a relationship with Sleepy Hollow, as they both have female characters of colour who take no shit. It also helps that the Twitter pages for both shows' writers have been engaging in a hilarious Twitter "feud", with the CSI writers piping in.
"Solve For X" revolves around "P versus NP," the most notorious unsolved problem in theoretical computer science.
In "An Unnatural Arrangement," we meet a character with the unfortunate name of "James Monroe," and British Sherlock Holmes quips "Loved your doctrine." Britain was one of the only European nations to actually be in favor of the Monroe Doctrine.
Though the timing of the show may have justified part of their suspicion, Elementary since around about "M" has settled that it is not merely a rip off of BBC's Sherlock, despite what some fans still claim.
Considering that the CBS originally wanted to do a remake of Sherlock, had to drop the project because it couldn't get the rights, and then announced an own show based on what sounded exactly the same premise, the worry of the fans is understandable. Most of them were satisfied the moment they saw the pilot and it became obvious how far removed from each other the two shows actually were.
He Really Can Act: As of "Details", the fandom is more or less chanting holy shit, Jon Michael Hill.
HSQ: Irene is Moriarty. Fandom just about had a collective meltdown.
The pilot has Dallas Roberts play the role of the psychiatrist who manipulated the killer of the episode into murder. Roberts played recurring characters in The L Word, Rubicon and The Good Wife prior to this role. For many viewers watching the show after the initial airings, Roberts was obvious as part of the conspiracy because his next role after filming the pilot was a very important role as Milton Marnet in The Walking Dead.
In "Lesser Evils", the seemingly tiny role of the janitor was played by David Costabile, aka the Big Bad on Suits aka Gale Boetticher, a major role in Breaking Bad. A character who turns out to be an additional killer also falls under this, as he's played by David Harbour, of The Newsroom.
In "The Long Fuse", Lisa Edelstein (Dr. Cuddy on House) plays a business executive who turns out to be the bomber.
"Deja Vu All Over Again": Subverted. The show features Jim True-Frost and Andre Royo, both of whom will be very familiar to viewers of The Wire. Neither one did it.
"Snow Angels": We see the female murderer at the beginning, and she is shot by her victim right before he dies, but don't get a very good look at her because of a disguise. Later in the episode, we meet a girl played by Jill Flint of Royal Pains, who claims to be a stab victim, but who Bell takes in as a suspect. And yes, she did it.
"Blood Is Thicker": The wife of Gale the internet billionaire is the killer. She is played by Margaret Colin who recently finished a 5 year stint as Eleanor Waldorf on Gossip Girl.
Nightmare Fuel/Paranoia Fuel: In "The Deductionist", the serial killer internet stalks blonde women over a certain height, and then skins them. And the worst thing is that people like that exist in real life.
Periphery Demographic: In addition to Holmes fans and fans of the police procedueral, Elementary has gained an enthusiastic following from progressives, especially feminists, not just for Gender Flipping Watson and Moriarty, but also for subtle signs scattered throughout the series that the show's makers are earnestly trying to make the show progressive and pro-feminist. Judging by the enthusiastic response, they've largely succeeded.
The Producer Thinks of Everything: The show's first season was acclaimed by the fandom due to the several continuity nods (from the "Pilot" to "Heroine", the season finale), consistent Call Backs, details scattered around the episodes, good Foreshadowing, a significant soundtrack, and a solid story arc which developed in a right pace.
They Copied It, So It Sucks: By extension, these same fans believed it would be terrible because of this, long before the first episode even aired.
And the fact that CBS has done at least two made-for-TV movies that were attempts at pilots for modernized Holmes adaptations, both with female Watson analogues.
The Untwist: "We Are Everyone" might qualify as this for some people.