These days, some uni jobs in Korea that previously used to be good jobs are going downhill. Some things to look for (and ask questions about) and avoid:
1. Camps during summer/winter vacation. If they're paid at a reasonable rate (20 000 Won +/hour) then no problem. If not, I'd look elsewhere.
2. No housing or housing allowance. If this is the case, your salary should be at least 3 million Won. If not, you're getting ripped off. Alternatively, living in a student dormitory is a recipe for disaster.
3. Teaching kids/uni students. Some unis are going uniwon (Uni+hagwon) style. Chances are, you'll spend most of the day teaching kids and have very strange hours, like in the early morning and late at night.
4. Mandatory weekly meetings or "English cafe" or "free-talking hours" work. This will get annoying fast. A small amount goes with the job but hours of it every week will make you hate your life.
5. A massive turnover. If the uni is hiring 10+people, there is likely a reason why so many people left the previous year. Ask some questions on a place like www.eslcafe to find out why. There is perhaps a good explanation, such as the uni is just expanding their programs. Most good unis will have very low turnover and hire only a handful of people each year