i'm very surprised by the reviews this show got. Of course is not for everyone, the show takes its time to get where it wants. People who wants action by the first or even third episode will not like it and find it very boring (and that's ok). I would recommend people to pay more attention to what is happening in the show, a lot of details is being explained throughout it but it really needs to pay attention.
For the characters, some people complain that Taeoh becomes the good one, while Inha the bad one. Life is not that simple lol. The show is quite clear that none of the main characters are one thing or another, since the second episode it shows that the three of them are moved by their own greedy. Inha doesn't do things out of blue, he was always a emotional person, that's why he start to like Taeoh from the beginning and falls in love for Hye-won with just few interactions. He is quite a obsessive person that is doing things without thinking from the start.
Hye-won, I agree, could have much more impact in the show. Her development gets lose every time something happens with Taeoh and Inha. She is a good character and should have more time for us to see her plans.
(I won't even talk about people saying that is bad Hye-won and Taeoh have kissed a day before the marriage, of course is not right to do, but yeah people are human and make mistakes - this doesn't imply that you should kill someone and put the blame into your ex-friend)
A lot of dramas struggle when doing the Succession plot and I won't say that Impossible Heir does it the best, but for sure it makes much more sense than what has been done in much others.
Recomend people to give it a try until the episode 8, when I think it really makes everything more interesting and, since it only has 12 episodes, I don't think one would be wasting much time doing so.