These aren't necessarily full-on plot holes, but stuff that's odd or really hard to believe. In general, the omniscience and omnipresence of OZ tends to be way over the top, especially contrasted with their miraculous absence at other times.
How does Woo Hyung Chul turn into Woo Jae Pil during the chase after attacking Bong-Yi? He must be wearing the exact same clothes and know the escape route of his son in advance and predict the attack on Bong-Yi and predict the resulting chase and not be spotted by his son as he runs past and pop out of the same corner right after. (Woo Hyung Chul gets home wearing his normal lawyer clothes, where he meets Ko Moo Chi pointing a gun in his face.)
Why does Woo Jae Pil try to kill Jung Ba Reum with a pipe if he wants to be arrested instead of his son and take the fall for him?
In episode 10, Jung Ba Reum conjures a delivery truck from thin air to precisely crash into Woo Hyung Chul's vehicle from a side road. How does he research car theft techniques, find a suitable unused vehicle, break into it, start the engine, and essentially overtake the lawyer's getaway using some shortcut roads all while Woo is driving away at high speed?
In episode 12/13 Jung Ba Reum knows ahead of time that Lee Jae Shik is another not properly punished serial killer, and declares him his next target by putting his DNA onto the murder knife with Daniel Lee's help. It's absurd how he knows that and they can achieve the "DNA transplant" so to speak.
In episode 14 Detective Konam (Myung Ko Nam) enters meat-man Kim Byung Tae's home (!), has his key (!), opens his music box (!), and realises instantly that it's about the murder of a kid 20 years earlier (!). Just what?
In episode 16, the magical OZ cleaners remove a body impaled on a metal rod and get rid of all evidence in between 20 and 40 seconds, while Jung Ba Reum chases a car out of the parking lot. That's better than a Formula 1 pit stop crew, isn't it? Where do they even come from? Do they emerge from the parking lot asphalt and sink back into it?
The absurd reason why Kim Joon Seong is killed is because Sung Yo Han wears his jacket and has pictures of the serial killings committed by Jung Ba Reum at his home. I've never started randomly wearing a friend's clothing that they forgot at my home.
More importantly, is there any universe in which, after you hack into a secret government black ops unit's data storage server, you go and PRINT THEIR PHOTOS so that you can pin them to your wall like they were polaroids? And so that any random grandma can steal such a printed (!) photo from your basement?
How and why does the Jesus Mouse that died while meticulously observed by Daniel Lee revive itself and exit its cage, as seen in The Last? How can Han Seo Jun even send mice from prison? Is this all just meant to support Jung Ba Reum's hope in his very last conversation that he can be born as a 'normal' person in his next life and be with Oh Bong Yi?
When Jung Ba Reum wants to commit suicide in his own house, OZ (?) knocks him out in just that moment, but then Daniel teleports there to talk to him when he wakes up (and take his gun away). Considering the level of OZ surveillance of his house, how is that possible? How would Daniel know when to come? If Daniel can know, OZ must know. If OZ knows, Daniel can't come.
(I don't think it was Daniel Lee or Choi Hong Joo who knocked him out.)
It's way over the top how the mothers of Woo Hyung Chul & Sung Yo Han & Jung Ba Reum met each other, and how in the show's flashback past Jung Ba Reum & Sung Yo Han, Jung Ba Reum & Han Seo Jun's aggressive rat/mouse, Jung Ba Reum & Choi Hong Joo, Oh Bong Yi & Sung Yo Han & Ko Moo Chi, Sung Ji Eun & Lee Jae Shik meet.