Right off the bat, my review is much higher than others I've seen.
And I'll admit that a lot of the things I liked about this show were circumstantial stuff... What do I mean by that?
The past few shows I've watched were very "light" ones that I could easily predict, so I was in such a mood for something heavier and more thought-provoking. This show brought that to me along with a bunch of other... things -_-
Let me just get straight to the point...

Story 〆(・∀・＠): I was so excited about this show before I watched it. It had a bunch of actors I was familiar with, the premise of parallel worlds was hella interesting, and just the whole aesthetic was beautiful. I waited till after it finished airing, so I didn't have to wait for a new episode each week, but that left me time to hear other people's reviews on it.
And that's when a big red flag was raised on how this show might now be what I expected. I ignored it and went on with it regardless, but after wrapping it up, I could see what everyone means.
The beginning, to me, was not that bad. I really loved the world-building and all the characters that were introduced. Sure the story's main conflict wasn't revealed until much later, but for some reason, I didn't mind watching this beautiful world come together. I mean seriously!! I would love to watch a show all about the Kingdom of Corea and the world it resides in. Sure there were some questionable character choices but nothing too out of the ordinary.
The problem with this show comes in the second half... more specifically, episode 13 and beyond.
The show could be a little confusing since the setting was continually changing from one world to the next without any clear way of knowing which is which. Unless it's explicitly stated or some prominent symbol is shown, you can get confused about exactly where the character is. So you always have to pay attention and use your head—something I wanted in a show at that specific time. But even with all the other not so clear choices and events that happened, the show didn't become difficult for me to comprehend until they brought in time travel.
THAT is when things went wrong for me.
The writers just kept adding new things into the already full supernatural mix. You already had parallel universes, but now there is time travel, alternate timelines (I think), and moments that I still can't understand even after doing so much research!!! Like... why writers!?
The characters started becoming unpredictable (not in a good way), and so many things were added just for a dramatic flair without consideration of what was already standing.
* sigh * It was like having to solve some complex math equation.
But then again, I always found a way to explain things to myself and even went out of my way to look up other people's theories and explanations. I think just doing that was somehow really enjoyable for me.
(I sound messed up... right) XD
I'd also like to mention how the scene order for this show makes NO SENSE!!! What I mean is that an episode will end on a cliffhanger, and then the next one will begin god knows where. They try and build things up while leaving other stuff a mystery. An example is how they'll show a scene, you watch it through and think it's done, but then two episodes later they'll cut back to it with whole new dialog that the writers wanted to be left a surprise...
like... NO... that's not how scenes work!!
Putting together everything I just said: the beginning was enjoyable since I personally enjoy fantasy world-building, but other stuff got incredibly confusing towards the end. After research and just talking to myself, I can put together 98% of the scattered pieces, but I know most people won't go out of their way to do that. So instead, this show is going to seem like an incredible unplanned out mess.

Acting ｡゜(｀Д')゜｡: As I mentioned earlier, most of my problems are in the writing and filming itself. I personally enjoyed the actors a lot. I didn't always like the characters, but that's because of the writing rather than the actors. I've seen these people in other works and know that most of them are incredibly talented. And when having to show it, they can.
For example, Woo Do-hwan had to be two different people with two different personalities. He pulled it off really well, and everything from posture to just tone of voice was carefully portrayed.
So I know that the flatness and unpredictability of a character comes from the writing instead of the actors.
Of course, some people may know more than me since I'm not an expert on acting, but using what I saw from the past, I know that these people have talent and don't want to say they don't because of this show's poor writing.
They tried hard in my eyes.
The relationship chemistry was... okay, I guess.
The romance kind of just popped up out of nowhere and shocked me a bit, but it was cute to watch nevertheless.
I liked the bromance and trust between some characters much more than the couple stuff.
Too bad the show was too focused on it, which ended up sacrificing a lot of what I loved...

Music ヾ(⌐■_■)ノ♪: I really did like the music. I think the music and all the scenery fit well together.
There were those happy songs that played at happy moments and sad ones during sad moments.
What made me raise the score a bit was the songs that played during the opening and ending portions of the show.
I could honestly re-watch the opening over and over again! The music and the whole abstract editing bit looked so flipping cool.
I know that doesn't connect much to music, but It was just soooo cool!
Overall, music was more enjoyable than those from other shows I've watched, but nothing revolutionary.

Other (ง°ل͜°)ง: Oooooof
Where do I begin with this mess?
I'm just going to repeat that I didn't mind having to solve a lot of the loopholes. For some reason, I found it fun and brain-racking, which was something I wanted in a show at that specific moment.
I was still irritated since it definitely was much messier than I would've liked, but not so much to where I wanted to drop the show.
The parallel universes bit wasn't the part that was hard to grasp... it was everything else. What the legendary flute could do, the boy who likes yoyo's, memories from alternate times, just the whole shebang was so disorganized.
From that disorganization comes so many unanswered questions and plot lines that just don't make one ounce of sense.
I will not say which ones, but just be warned that past episode thirteen, your brain will want to explode.

Although I've listed so many problems (that were major ones), I still couldn't give the show that low of a score.
I did like a lot of it and would watch it again one day. Maybe if I watch it again, then things will finally make more sense XD
I'm a huge fan of world-building, and TKEM brought me something so interesting that I just wanted to know more about the kingdom and its monarchy.
I don't think I'd recommend it since the main things I loved about this show are more focused on my interests rather than what I'd think most people would like. In fact, I wouldn't recommend it to any curious person.
This show had so much potential and was beautiful in all things except the writing and editing.
If you're ready to use all your brain power, then go for it. But otherwise... run
Happy Watching <3