Early on, before the outbreak inside the train, Su-an fears that zombies are near because she saw a rabid citizen attacking another human in the station. However, Young-suk just dismisses her guess because he believes that zombies don't exist in modern times. In this statement, Young-suk actually refers to the earliest types of zombies in pop culture — the Voodoo Zombie controlled by necromancy. What he doesn't know is that the zombies popularized by George A. Romero are usually caused by virus infections, something that very much can happen in modern times.
One of the bigger complaints about the movie's beginning is the fact that the first infected woman ran onto the train right behind the station attendant without him even looking up, despite the fact she was running and breathing loudly. Did he not notice her? Or, possibly as likely, he didn't think twice about it. It IS a train station, and it was just about to depart. Having people sprint in onto the train at the last possible second would be an everyday occurrence. And, it being a train, he wouldn't have bothered with her later and assumed whoever was inside would check her ticket later. And even though she did collapse and start gasping loudly, the train windows and body are very thick and muffle sounds coming through, to the point only Su-an noticed the security officer being attacked later, so she could have easily been ignored or not heard at all over the usual sounds of a train station.
During the Korean War, Busan (AKA Pusan) was the site of the Battle of the Pusan Perimeter, in which the U.S. and South Korean forces tried to halt the North Korean People's Army overrunning the entire peninsula. They held out long enough to be reinforced by United Nations-led forces landing on Inchon. In this film, Busan is used as a safe-zone by the Republic of Korean Armed Forces, with the outskirts used as a perimeter against the infected. YMMV and Awesome on this as a Historical Call-Back, but worth the mention.
The first scene of the movie reveals that animals can get infected with the zombie virus. Though that never comes into play in the main plot, that means there are MANY more ways for the virus to spread. You have animals on the ground (like deer and dogs). You have birds. You have mosquitoes, who don't have to be "zombified" to spread the plague; they're just spreading infected blood around. Unless there's a cure for the virus, the entire world will fall to the virus soon.
Unless the virus is similar to rabies (as these zombie viruses often are), in which case it can probably only affect mammals. Probably.
Even that still means that any small mammal (such as rats or squirrels) will be able to worm their way into uninfected areas and spread the virus. Unless some major pest control is implemented, humanity will have a hard time of keeping the virus out.
It's implied in a news article that Seok-woo reads that at least fish can be infected, but perhaps any non-mammalian animal will just die outright from infection. If that is the case, then possibly any animal can be infected, but if it isn't a mammal it will be 100% fatal, which is still pretty bad, if infection is guaranteed by bite or scratch. Also, if it only can zombify mammals, then dolphins can be zombified.
