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.
Author On Board: Making the Edward Snowden expy a self-aggrandizing murderer who was willing to sell 14 men out to save himself.
Breakout Character: Clyde the turtle is oddly popular for a character who appears only slightly more often than Mycroft.
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.
Was the second season finale brilliant or awful? Was the second season in general as good as its predecessor or an uneven, heavily flawed season? Most fans seem to lean towards the latter, especially with the implication that Mycroft pulled a Reichenbach fall and not Sherlock by faking his death to save the day, despite RF being a pivotal point in Sherlock's character. Not to mention that Joan's making plans to move out of the brownstone, stating that she needed to grow away from Sherlock despite essentially one-upping him all season. And then Sherlock is seen with drugs he'd stolen from an earlier episode, contemplating using again!
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.
A source for some Broken Base argument, too. Sherlock and Joan's season two relationship: a necessary development or suffering from completely unnecessary Conflict Ball? It was almost universally regarded that Joan frequently calling Sherlock out on his faults in season one was a good thing, humanizing Sherlock and not letting him get away with breaking the rules and acting antisocial. In season two, on the other hand, Sherlock is constantly being rebuked by Joan for his behavior, even in situations where Joan would usually use tough love and reasoning instead of just scolding him. At worst, this made Joan into an unintentional Creator's Pet, as she is almost constantly in the right and never gets the same treatment that Sherlock does. In the first season, Sherlock and Joan were a team and depended on the support of one another, and the constant presence of a Conflict Ball in season two seemed almost a regression in their characterization from their partnership in the previous season. On the other hand, other fans viewed this conflict as necessary, since Joan needed a reason to leave the brownstone, especially since there doesn't appear to be a Mark Morstan what with her already having an ex with the surname.
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 many fans.
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.
The stupidity of the rivalry has reached astronomical bounds, especially since some die-hard fans of Sherlock insult Jonny Lee Miller's performance as if they're paying a service to Benedict Cumberbatch by doing so... Seemingly not understanding that the two are good friends and performed in a play together. Tensions have calmed only at the second series, where even antagonistic fans admit that Elementary isn't that bad.
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.
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.
"No Lack of Void" features Garret Dillahunt(AKA Cromartie and Burt) as the killer of the episode.
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.
It's also praised for being one of the few shows with an Asian lead character.
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.