At first I wasn't even sure if I was going to watch this until the end after seeing the first two episodes and were about to drop it. Now I'm glad I didn't as it managed to entertain me and I ended up liking it.
I'm far from being a medical profession but still, I do know a bit about medical stuff so maybe I'm more difficult to please when watching a drama with medical theme and tend to be also more critical.
While I cringed here and there about some things that just didn't seem logical to me the drama was enjoyable in total.

I didn't know and haven't seen the Japanese Original from 2009 when I watched the Korean Remake so that's possibly why I was more compliant than other reviewers who watched the remake after the original. Still, now that I watched it I have to adjust the rating. The Japanese Original is indeed better.

The Korean Remake is definitely not bad but it included an unnecessary second male lead to cause a "dramatic" love triangle and that was just dumb. The story doesn't need such nonsense and it made things just worse in the remake, things that would've been fine without this element that Korean Scriptwriters seem to love but is mostly annoying to no end, at least for me. The storyline is really interesting on its own and doesn't need any adjustments in my opinion. The J-Drama has some depth that lacks in the Korean Remake which is sad cause it gave the drama so much.

I like the characters and think the actors did a great job. The medical theme is not perfectly accurate but quite good and I've seen worse.
The whole time travel, parallel universe stuff was a bit confusing towards the end and I have to admit that at some point I lost focus and didn't care much about how it would be explained in the end. As anticipated the explanation wasn't really satisfying anyway so I didn't dwell on it. It was more logical in the J-Drama and I think it might've been better to just keep that instead of changing it to something that is confusing.

The music was not really outstanding and sometimes it felt a bit out of place and was not matching the scene but it wasn't really throwing me out of the scene anytime so it's okay. In fact the song "Last Love" sung by Song Seung Heon was very nice.

Despite it's flaws I like the drama and enjoyed watching it. I think it's worth a watch if you enjoy historical medical drama like me, but I would recommend watching it before the Japanese Original because the Korean Remake has some changes and most of them are not good but rather the opposite.
For me it's perfect proof that sometimes remakes are not needed and that an original is still better. Truth is, that it's hard to do something better what is already very good. In this case the attempt failed. I probably won't rewatch the remake again, at least not completely but instead picking the scenes I liked.
I still give it a solid 7.5 stars rating, cause it gave me a good time when I first watched it.

Edit: a little over a week after the original publishing of the review