This is a very well-made thriller. After first watching, it seemed not to make any sense at all to me, and I got quite angry at it.
But then, I went back to it, and patiently went through some of the scenes again to catch the detailed hints. Man, it sure isn't easy to figure them out ! Hollywood thrillers are very in your face with plot hints. This one is far more subtle, and the viewers have to really catch the details themselves.
Since there are many negative comments here because of the impenetrable plot twists, I will list what I found out so far (it's really more of a puzzle than a straightforward thriller, think "The usual suspects"):
At the beginning of the film, the detective removes a button from the dead body of a boy who fell out of a window; the other one is missing. The missing button is the one he sees Chae put into the drawer in the video towards the end of the movie. When he gets into the room 702 where the victims were dissected, he imagines how she pushed the boy off the window. She does it because the boy had been spying on her. Without this link, the detective wouldn't know Chae was in that place, so it is crucial.
On the photo, there are the two women, Chae and Seungmin Oh, together will all the male victims, each holding a bottle with fish, similar to the one that Chae gave to the detective before she left for Paris towards the end. They are standing in front of a water tank. When the detective first went to the home in the woods where Chae was hiding after being attacked, this tank was briefly shown. It was not recognizable as such, but the metal corners were standing out. The detective remembered it from the photo.
The tools that were packed and removed from the room 702 where the detective's partner was killed were found in Seungmin Oh's apartment by the police (before the scene at Tower records). Therefore, she was the one who killed him.
The body missing the head inside the tank is Chae's father's. His head was in the freezer that the detective's partner found just before he was killed. Over the phone, he informed the detective that the head was Chae's father's. His killer (Seungmin Oh) removed the head from the freezer before leaving.
This implies that both women were using the room 702 for the killings. They were partners in those crimes. Seungmin Oh has burn scars on her legs (shown before she leaves for Tower records). She is Chae's childhood friend who set the house on fire. Chae was lying when she said that friend was a boy, in order to cover up Seungmin Oh (her partner in crime).
The men were all former boyfriends of Chae, according to what she said. However, they are shown united on the photo, together with Chae and Seungmin Oh. They are standing in front of the tank that contains Chae's father's dead body, in celebrating pose. This implies they must all have been complicit in killing him. Her father was the first victim, and contrary to the others, his body was kept hidden. From the way he was portrayed, the former boyfriends must have had reason to hate him; also, she must have manipulated them in wanting to murder her father.
The plastic bag that led back to her father was placed to make her father the main suspect for the killing of the young men. Presumably the two women killed them in order to stain Chae's father's reputation (he is a very famous artist). Things went wrong with this plan when the detective's partner discovered her father's head in the freezer just before he was killed, and informed the detective about it. Knowing that her father was dead, he wasn't a suspect any longer for the police. This was the point where Seungmin Oh understood that their plan was unraveling.
The person in the car who was attacking the detective in the rainy night, after he finds one of the victim's place, is Seungmin Oh. The police (towards the end) identify her as the owner of a car that was caught speeding on that night.
Seungmin Oh knows that the police has tracked her down, after seeing them at her workplace. To draw attention away from Chae, she spills the blood in the bathtub, and makes it evident that she is the murderer. She still wants to cover Chae.
Chae's call to the detective telling him she will meet Senguin at Tower records is a setup. She says "just because I was thinking of you", which is not typical for her. He was supposed to kill Seungmin, this was the plan of both women.
There is an enigmatic short scene 30 min before the end where Chae and Seungmin Oh meet for dinner, together with some young men (just after the killing of the detective's partner). Seungmin asks Chae "Did you really go to the hospital to die ? You are not the suicidal type." It looks rather like a memory, and the men present at the dinner might have been the victims. It might imply that the women were ready for suicide, but that Chae wanted out, and that Seungmin was ready to take the blame, in order to give her an alibi.
All in all, it started to make sense to me after moving through the film back and forth on my ipad. This is the first time I had to do this to understand a movie. While it was frustrating at the beginning, this is all looking a lot more interesting now.
Finally, the original title is "Telmisseomding", and was translated to "Tell me something". Much rather, it might mean "They'll miss something".