Having experience with real court (Russian, though, not Korean), I can tell, that the series breaks quite a few protocols, that need to be followed even when keeping in mind, that trial is a TV show in the show's lore.
For example, the way prosecutor is shown here is like he is a pompous advocate, which is a US cliché. But prosecutor is representative of the state (government). It's not a representative of a victim as what you commonly see in US shows. I mean, he may share some of his biases, but not like that. Surely not during initial presentation of the case, which is meant to be a list of facts. I think even US shows try to follow the protocols much more closely than that.
So, no I was not able to believe in the "trial" here at all. Otherwise, though - quite high quality based on the 1st episode. Sound design, cinematography, actors... Can't say I've noticed anything too damning in any of those. And the concept itself is interesting. If only trial did follow the law as characters suggest, though...