Your #2 problem
A rather frustrating point for many new arrivals in Korea can be public bathrooms. Whilst you can expect modern, Western style facilities in hotels and even Japanese-style futuristic contraptions in the top-tier department stores, and use of these is growing, many public facilities still utilise Asian squat facilities.
However awkward this may be to beginners, do not complain so hastily, for this can pale in comparison to the #2 problem: paper! A curious hangover from postwar poverty, Korean toilets do not typically provide any form of paper, nor bidet alternative. Instead, patrons were expected to provide their own. Bathrooms usually have a single dispenser, but you'll find it outside your stall or perchance in the form of a vending machine or attendant selling pocket packs at the door. Pocket packs can also be purchased from almost any convenience store, and it is strongly recommended you keep a pack on you--in your pocket perhaps.
Your nose however may alert you to a third oddity, and this one can be the most uncomfortable one. Whilst most plumbing can perfectly handle the pitifully thin paper provided, many still put up a fight! If you see a trashcan beside the bowl, be aware that you are expected to stash the soiled tissue safely in its centre.