The Lieutenant with Amon, especially in the finale. His reaction when he realizes what Amon really is practically screams "spurned lover".
Lieutenant: [Amon] You traitor! I dedicated my life to you!
In the same episode, the Lieutenant's distinctive weapon can be seen on the boat Amon and Tarrlok use to escape the city. Makes you wonder if they were planning to escape together before Amon was outed as a bender.
The fact that Korra has been confirmed to be canonically bisexual, as she begins dating Asami at the end of the series, lends an extra level to much of her moments of homoeroticism, since she could very easily be attracted to the women in question.
In Book 1, many see the scene in which Korra rides in Asami's race car as very shippy. More so the scenes before and after where after bonding, Korra removes the one insult ("prissy") she had used to describe Asami. On Asami's part there is her trying her dead best to become friends with Korra, and even after everything bad that happens to her, because of her friendship with Korra, Asami still states that she likes Korra.
Asami makes it clear to Mako her problem is not with Korra but with him for keeping secrets from her and not being honest about his feelings.
In Book 2, when Varrick suggests that Asami smuggle weapons to the Southern Water Tribe to help fight against the Northern Water Tribe, Asami agrees without hesitation as this will both help Korra and save her company from bankruptcy. In contrast, Mako tells Raiko that Korra intends to go behind his back and get the United Republic Army to help fight against the Northern Water Tribe, thus hindering Korra's efforts to help her family which leads to their first breakup. While this is not quite a shipping moment it does show how far Asami is willing to go to help Korra, aiding in a war that the United Republic has stated that it wants nothing to do with, while Mako takes Raiko's side and tries to keep the United Republic out of the war.
Korra and Lin Beifong hold hands in "And the Winner Is". There is also the scene in "Out of the Past" where Lin, still injured from the Equalists' attack on the pro bending arena, immediately gets out of bed to go searching for Korra after she hears on the radio that Korra was kidnapped. And there is the fact that Lin chose to give up her bending rather than sell Korra out - and then Korra is nice enough to restore Lin's bending (in fact, Lin is the first person to get her bending restored thanks to Korra).
Korra and Opal's dance-like airbending training. Some fun can also be had with the fact that Korra interrupts a moment between Bolin and Opal.
She is also the person who encourages Opal to try and speak to Lin one on one in "The Metal Clan".
Kuvira has a habit of putting her hand on people's shoulders when speaking to them, and she does to this to Korra during their first meeting.
As pictured, in "The Last Stand", after the spirit vine cannon explodes and Korra and Kuvira end up in the Spirit World, Kuvira wakes up in Korra's arms with an amusing shocked reaction at being so close.
They then proceed to have a heartfelt talk about their feelings and walk out of the Spirit World with Kuvira leaning on Korra.
Whch has an extra dimension of subtext in light of the finale where Korra walks through the same spirit portal hand in hand with her canoncal same-sex love interest Asami.
It's a bit of a stretch, and it's unclear whether Raava is even technically a woman, but the spiritual union between them, Korra's distraught reaction to Raava being hurt and joy at seeing her again in the spirit world are fairly shippy, especially in light of the slightly romantic undertones Raava had with Wan.
"I have always been inside you."
As a callback to all the Ho Yay in Avatar: The Last Airbender, Zuko and Aang remained best friends, according to Iroh. Korra even goes so far as to say that Zuko knew Aang "better than anyone else." Including Katara?
In "The Coronation", Prince Wu seems to really be looking forward to the idea of living a hedonistic lifestyle with Mako and later calls Mako "his big tough guy".
After the fiasco at Little Ba Sing Se, Wu asks Mako to carry him home.
In "Reunion", Wu is captured while taking a bathroom break without Mako. Mako's reaction? "The one time I don't watch him pee, this happens!"
The last time Mako was slamming a Mook against a wall, demanding to know where somebody had been taken, that somebody was his Love Interest.
Wu is also constantly hugging Mako when he gets rescued and says "Mako, I didn't know you came from money" in a rather suggestive/flirty tone.
In "Remembrances", Wu is a little too eager to learn more about Mako.
According to the DVD commentary, the background idea with Wu and Mako was that Wu saw Mako in the newspaper as a “hero cop” and said “I want that guy!”. Love Before First Sight?
A lot of people could not help but notice the romantic undertones in Zhu Li's slavish devotion to Varrick, so when she renounces him and pledges loyalty to Kuvira, saying that Kuvira, not Varrick, has "the most amazing mind in the world", and that he "never appreciates me", finishing up with "I want to dedicate my life to you" it comes across like a neglected girlfriend angrily dumping her man and running into Kuvira's arms.
Then there's the fact that Zhu Li served as a decoy Kuvira by sleeping in her bed.
When Varrick and Bolin meet in "Rebel Spirit" Varrick gets really close to Bolin's face at one point, puts his arm around Bolin's shoulder and says he likes him.
When Bolin becomes Varrick's assistant after Zhu Li betrays Varrick, Bolin saves Varrick's life and then Varrick kisses him on the forehead.
In "Reunion", Varrick rides on Bolin's back. After Bolin's rousing speech, they decide to trade places.
In "Operation: Beifong", Lin tosses Su's family to Bolin. He catches Wei bridal style, their eyes meet, and Wei smiles and gives him a friendly bro face pat.