The two main characters use a simple rope to trade food and other items between their respective apartments. This wouldn't be possible in reality without the use of some sort of pulley system.
When the main characters chat through walkie talkies, the iconic Tom Cruise rock climbing scene in Mission Impossible was referenced. They said it was in Mission Impossible 3 but the correct movie where this scene is from is Mission Impossible 2.
The main character stays in quarantine for almost a month but his hair color never changes, even though it is quite short. Also, the female police officer was bitten from her throat and she didn't scream as she should have and pointed her gun to her head in silence instead.
Just before the power goes off in Joon-woo's apartment, he looks out the window to see a missile hitting part of the city. There's a bridge between where he is and the explosion, with cars running at normal speed in both directions, as if there's no emergency whatsoever.
After the power to Joon's apartment is cut, it is unclear if the power was ever restored, but his cellphone is shown to always be on even when the ordeal has lasted 15+ days.
The electricity gets turned off halfway through their struggle to survive; however, this is not reflected by their electronic use such as cell phones. While the speculation of portable chargers grow, it hasn't been shown in this movie.
The main character pushes the refrigerator against the front door. The problem is that the door opens outwards, as shown in several scenes, and the refrigerator really blocks nothing.
When the main character's apartment is broken into by the zombie, the display on the refrigerator is active and showing the temperature of the fridge and freezer. Either that is an extremely long cord or it runs on batteries.