I had mixed feelings about Empress Ki. I nearly abandoned it twice before episode 19. But now, after watching it up until this point, I can confidently assert that this drama is made of little other than idiot plots.

Acting/Cast
Let's start with the good. The acting is superb - in particular, the Emperor is played extremely well. I despised the character with a passion, but that was partially because of how well he was acted. Seung Nyang is acted fairly well, although the particular acting style - somewhat more rough - works much better during the first few episodes before the plot entirely devolves into attempts at courtly intrigue. The minor characters are often a bit overacted, but that actually works - it adds to the comedy in the smaller scenes fairly well, and characters like Eunuch Bang really help to bring together Woo's other retainers.
Even the character voices are good - characters have a certain style of speaking or acting that stays consistent throughout, and you can really feel their personalities shining through during the series.

Music
The music is nothing special. There are fewer than ten tracks that play with little variety starting from the same point, so it gets to feeling quite repetitive, especially when watching several episodes and hearing the exact same song from start to finish several times.

Story
I will admit, I don't watch TV for the characters. They're nice, but ultimately, I watch for the conflict and the plot threads that slowly unravel across the course of a show. And... my goodness, but Empress Ki had some of the most poignant idiot plots I've seen in live action.
SPOILERS FOLLOW
An "idiot plot," as referenced by TVTropes, is any plot that could be resolved in a matter of minutes if everyone in the story were not an idiot. For a brief basis, Seong Nyang - a woman hiding as a man and serving the King of Goryeo as a warrior - is tasked with protecting the Crown Prince of Yuan, as those who control Yuan wish to use his death in Goryeo as an excuse to re-conquer the nation. She successfully protects him, and then - in Goryeo's court - The Crown Prince betrays her, siding with the Prime Minister, the man who wanted him dead. In the middle of Goryeo's court. Where the Goryeo military outnumbered the Prime Minister's men, and they could have killed him and sent the Crown Prince back as soon as he became the Emperor.
Okay, so he's an fool. But that's fine - he was already immature and pompous, so that's quite in-character for him.

Fast-forward a bit, and Seong Nyang has been sold into slavery and, her true sex revealed, is working as a maid in the new Emperor (former Crown Prince)'s court. Understandably, she wants to kill the Emperor for betraying her, getting her father and hundreds of other Goryeoans enslaved and killed, and separating her from her crush, the King of Goryeo. She gets right up to him and is convinced by another Goreyo maid that, if she killed him, everyone else from Goryeo there would be killed. That's honestly pretty reasonable, and after a brief conflict, she decides to accept that. Her next goal is to leave the palace, since she's still loyal to the King of Goryeo.
Here's where things go downhill for her too.
See, Seong Nyang is a seasoned warrior. She can go toe-to-toe with the best trained members of either country's armies. But it's as though putting on a maid's uniform has caused her to forget all her skills, or the far more risky maneuverers she pulled to keep the former Crown Prince alive. Leaving the heavily-guarded palace wouldn't be easy, but she has years of experience acting like a man, fighting, and infiltrating groups. Apparently, we are expected to believe that she is not able, or has deemed it "too risky," to try to escape the palace itself.
So that's a bit out of character, I'd argue, for a rogue who's utterly loyal to the King of Goryeo, but it's not strictly foolish.
And then it gets worse.
The Emperor (former Crown Prince) notices her. See, he developed a bit of a crush on her back when she was dressed as a man and protecting him in Goryeo. So now that she's miraculously turned into a woman, everything's looking up for him! Ignore the fact that he's a puppet controlled by the man who killed his father - he has a crush.
What follows is some of the most frustrating television I have had to watch in a long, long time. The Emperor proceeds to favor Seong Nyang while forcing her to care for him in increasingly creepy and intimate ways. And Nyang, a seasoned warrior who has topped a king before (King Simyang), just goes along with it. He acts magnanimous while refusing the few things she wants, and demands that she care for him like a child, taking up most of her time. He makes it utterly clear that he will never allow her to leave, even burning a letter of exit that she painstakingly obtained in front of her. I cannot properly explain how utterly frustrating it is to watch a warrior "trapped" - because she will not try to escape and she refuses to kill him - by such an arrogant narcissist, who himself is supposedly powerless.
And then there's the Prime Minister plot.
See, the Prime Minister - mentioned earlier - killed the new Emperor's father and brother. For some reason I still don't understand, he decided to let the new Emperor live just because he begged for his life (the Prime Minister presumably could have otherwise just installed himself as emperor). And now, since he's the antagonist for this part of the series, he's doing Bad Things and Stuff. He needs to be stopped. He also meets in private with the emperor almost constantly, in a secluded room where only the Emperor's personal guards are allowed. In the palace. With only the Emperor's allies.
Wait... couldn't the Emperor (or any one of his allies, really) just... stab him? The Prime Minister derives most of his power from threats and violence, but if he's dead, there's only his questionably-competent relatives behind him. But he's unquestionably committed crimes that - while hard to prove - are far from secret in the inner court. Emperors have rarely ever needed justification to kill underlings, and the Prime Minister commits capitol offenses almost daily. Literally, anyone with a competent assassin could have just killed him during one of these meetings, and I doubt any ministers - even those formally on the Prime Minster's side - would have shed a tear.
But unfortunately, nobody seems to consider this idea. He's this utterly impenetrable threat in the form of a weak old man who's constantly alone when he meets with the Emperor, a weak young man.

Honestly, it begs the question: who's running this country while everyone in the court is focused on either deposing the Prime Minister, finding a MacGuffin (bloodletter), or chasing after Seong Nyang, the most and least eligible bachelorette in the inner court?

ENDING
I will admit that I looked up the ending while deciding for the final time whether to drop this show or not, and it does *not* get better. The Emperor doubles down on abuse and combines narcissism with murder, Seong Nyang ends up turning villainess-ish somehow, and remaining few characters who I respected as relatively logical decision makers jumped the shark. If only the series had ended as it began, it might have been worth it to tolerate another thirty episodes; but upon reading how it turned out, I couldn't give it another chance.

SUMMARY
What started as a promising drama with interesting characters quickly spiraled downward after the first arc, with characters ignoring obvious solutions and focusing more on abusing or romancing Seong Nyang than doing anything actually useful. If you're watching more for characters and forlorn glances than plot, you might like this, but if you need a solid plot to enjoy a story, I'd advise you to give this one a pass.
I give Empress Ki a rating of one out of ten.