ETA: Click here to purchase the first season of Elementary.
ETA: I analyze the art history in the episode The Woman/Heroine.
Cut for major spoilers if you connect the dots.
You know the story involving Irene giving the fake Bruegel to a museum so she can own the real one? It echoes the Mona Lisa subplot in the Granada adaptation of The Final Problem.
However, I have not looked up any interviews with the writers, so I do not know if they intended this reference. I also think the aforementioned Bruegel painting The Blind Leading the Blind (look up at the beginning of this post) acts as a foreshadowing device for the main plot. Not knowing what Moriarty looks like, Sherlock blindly leads the equally clueless Watson and the NYPD around in their search for his arch nemesis.
One last observation. Unless I am misinterpreting his words, Sherlock praises Adler for holding “the vulgarities of the Modern era at bay”, but she had a Gauguin and a
Degas (I think) in her studio. I write Degas because the painting itself depicts a woman revealing her bare back to the viewer, a common Degas motif. ETA: C in the comment section writes that its Toulouse-Lautrec. Correct, for it’s La Toilette. This painting would also act as a foreshadowing device, for the story uses a woman’s back as a plot point. On Gauguin, if you look way in the background, Adler had his Tahitian Women on the Beach (seen above this paragraph) on her wall. Furthermore, I think I saw Irene restoring a Baroque painting. The dark background tipped me off. Strange, because in the previous episode, Holmes claimed she restored Renaissance paintings. The episode does not explain this, so did the writer and the production designer did not talk to each other
Honorary Mention: I haven’t read the original story, just the Granada adaptation, but I think the final (and oh so wonderful) plot twist references The Dying Detective plot twist.
ETA: Speaking of bare backs, they use Natalie Dormer’s back as a plot point.
ETA: I took out some broken links and a new one.
ETA: Tweaked a sentence.