First of all, why the heck isn't your topic showing up in the "Recent Discussions" section on the main page of Beyond Evil? :c
Second of all, I'm very eager to start the guessing game with y'all.
WHAT WE KNOW AFTER 4 EPISODES:
AS FOR THE MURDERS FROM 20 YEARS AGO
I think it's safe to say that Lee Dong Shik isn't the culprit (it'd be too obvious; he's painted as the killer on purpose), nor is Han Joo Won (as for the latter, he would've been too young to kill someone). Oh Ji Hoon (the young police officer) also cannot be the killer behind the murders from the past; he was too young, just like Han Joo Won.
AS FOR THE NEW MURDERS
Now it's a little bit tricky. Lee Dong Shik is portrayed as an unstable freak, but let's be honest: who wouldn't be traumatised after what he's been through. He was accused of killing his sister and a female friend without any proper evidence except for his guitar pick that had been found on one of the crime scenes. Among everyone, he's probably the one with the biggest desire to find the real murderer, as he's still associated with the killings.
Han Joo Won is not fully stable, either. He has a toxic father, and what was shown in episode 4, I began to wonder if perhaps he was abused as a child, or was in an accident in the past. What made me think that was the scene where Han Joo Won started to undress to clean his shirt that was covered in raw eggs, but he quickly covered himself when the chief barged in. I believe this scene was played out like that on purpose, and Han Joo Won has some scars on his body to hide.
I believe those two--since both of them aren't in their right mind--are capable of doing crazy things to catch the real culprit. For example, Han Joo Won used a woman to catch the murderer even though he knew very well she wouldn't be safe.
As for Lee Dong Shik, I think he'd be able to do even more fucked up things to catch the killer. Perhaps, he found Kang Min Jung's fingertips somewhere else, but decided to relocate them where they could be found easily, and where it would be easy to assume the victim's identity. So, he placed the fingers in front of Kang Min Jung's father's shop. Thus, the fingers were in plain sight, and by their location it was easy to identify their owner as everyone recognised the nails. Heck, I'd even dare to say that Lee Dong Shik could've found Min Jung's body, and thought of a genius plan to catch the serial killer. As Lee Dong Shik knows the killer's MO, he could've cut Min Jung's fingertips himself and disposed of her body where she wouldn't be found. I think he's pretending to be the real killer in order to catch the real killer. Because at this point everyone thinks he's the murderer, he doesn't care anymore if he's seen as one.
As for the young police officer Oh Ji Hoon, we haven't been shown much yet, but he also seems to be yet another freak in this drama. He claims to have seen Min Jung and her killer on the night she was murdered. He says Lee Dong Shik isn't the culprit, but he wishes he was. As corny as it sounds, perhaps Oh Ji Hoon was jealous of Min Jung's affection towards Lee Dong Shik, and that's why he wishes Lee Dong Shik was the real killer.
And lastly, this whole town is sketchy af. It all seems like a conspiracy of silence: the town people know something, but they choose to remain silent.