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.
Badass Decay: Sherlock spends the first season getting excellent character development and humanization thanks to his improving friendships while also speeding through cases. He spends the second season arguing with Joan, getting upset and anxious over the thought of Joan leaving him, getting jealous about Joan's relationship with Mycroft, and possibly turning back to drugs once Joan moves out.
Base Breaker. Irene Adler. A lot of fans already called her not being dead as well as Moriarty, but it didn't make it a popular decision.
In the second season, Mycroft. Some fans found him to be a strong character and loyal to the canon, while others found his plotline tedious and overlong and his relationship with Joan a complete Ass Pull.
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!
Complete Monster: Moriarty, aka Irene Adler, is a self-described "Assassin Pimp" who arranges murders both at the behest of others, and to fulfill a private agenda. In "M." Moriarty sends Sebastien Moran to kill two people by suspending them from their ankles and draining all of their blood, then betrays Moran to Holmes in the hopes that Holmes will kill him. In "A Landmark Story" Moriarty has Daniel Gottlieb shock a man to death by hacking his pacemaker, drop an air conditioner on another, and use killer bees against a woman with a severe allergy; by threatening Moran's sister, Moriarty is able to force Moran to commit suicide. Moriarty also has Isaac Procter kill a man who served as a Body Double, then sends assassins after Procter in "The Woman", before killing him personally. Outed in "Heroine" Moriarty kidnaps the daughter of a Greek shipping tycoon, in order to force said tycoon to murder two Macedonian nationals, all to prevent Macedonia from joining the EU, and make a large profit by investing in Macedonian currency. Couple this with the fact that Moriarty is responsible for causing Holmes's breakdown in the first place and that her crush on Holmes is more about viewing him as a piece of artwork than anything else, and there is no reason to consider Moriarty anything other than the very worst that Elementary has to offer.
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.
Fan Dumb: Some fans were outraged when Joan was kidnapped in the second season, thinking that it was turning her into a Distressed Damsel; these same fans seem to have forgotten that Sherlock was kidnapped in the first season, with Joan saving him (thanks in part to the perp's blunder).
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.
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.
Positive Discrimination: In contrast to the first season, when Joan made mistakes while going out on her own as a detective, the second season saw Joan smoothly running through cases, matching and sometimes even surpassing Sherlock, and continuously calling out Sherlock while rarely making mistakes herself. This seems to be a combination of both Pandering to the Base (for a fandom that idolizes Joan) and Conflict Ball (since the plot demanded Joan and Sherlock have conflict incongruous with their behavior in the first season). No one's denying that Joan is extremely intelligent, but it's tedious to see such a well-developed character be reduced to "Bad Ass who takes no shit and never makes a mistake, ever" by fandom and writers alike.
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.
Sophomore Slump: The second season did justice to the first, but was nevertheless marred by Conflict Ball-induced stupidity, Sherlock and Joan bickering rather than getting closer like fans wanted, and Mycroft's overlong plotline (including a somewhat unbelievable romantic subplot with Joan).
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.