They've done more than "minor incidents"
They've conducted bombings that killed quite a few South Korean politicians. They kidnapped people and held them from years, not only from South Korea but also from Japan. They also had agents blow up a South Korean airliner (killing 115 people) back in 1987 to scare people from attending the 1988 Seoul Olympics. One of the agents was captured and confessed. North Korea has also done some pretty screwy things like capture the USS Pueblo in international waters and send midget submarines on covert missions to the South.
I've read some recent articles that claim the North Koreans aren't really crazy, but so far, I'm not convinced. They sure sound screwy to me.