One of the least appealing aspects of the season is Sherlock's brother, Mycroft. Played by Rhys Ifans, Mycroft becomes romantically involved with Joan, leading to triangular jealousy with Sherlock (who hates his brother) and general emotional friction.
There are a number of problems with the arc. The show is circumspect about refusing any romantic tension between Joan and Sherlock—a commendable counterintuitive choice which is somewhat vitiated by the jealousy plot. The real stumbling block, though, is that Rhys Ifans is about as attractive as a dried rat with a combover, which he unfortunately resembles. It's not just his physical appearance that's off-putting either; as an actor, Ifans has no discernible charm or spark. He's smug and irritating, but without Johnny Lee Miller's mercurial awkwardness or vulnerability. It's just about impossible to figure out what on earth Joan sees in hims. She's movie star stunning (since she's played by Lucy Liu), brilliant, and possessed of a low key but devastating wit; he's a bland nonentity. They have no chemistry either; it feels like they're together because somewhere some writer couldn't figure out what else to do with them. Their bedroom scenes go past uncomfortable and on into viscerally repulsive.
If Mycroft had some charisma, or if there was some real connection between them, then there wouldn't be any problem with Joan having a romantic interest, obviously. As it is, the storyline seems to be handing Joan over to Mycroft in order to generate angst for Sherlock; she ends up being there in order to make him react. It's certainly not as grotesque as the last season of BBC's Sherlock, where every character has no purpose but to stoke the Cumberbatch psychodrama. But in its first season, Elementary did a lot of work to show that Joan was an equal partner, not Sherlock's accessory. Her relationship with Mycroft undoes some of that work, because it's so clearly a means for the writers to tweak Sherlock, rather than to give Joan an interesting or believable relationship in her own right.
The homely guy/hot woman pairing is semi-ubiquitous in media because the assumed audience tends to be men, who are presumed to enjoy the fantasy of being with a movie star. Elementary doesn't go very far down that road; jis blahness is less fantasy for male viewers and more just indifference to female ones—or at least to Joan's perspective. What does she see in this aging, unattractive, smarmy guy? The show doesn't respect Joan, or the viewer, enough to figure out an answer.