I've spent time conducting basic flight training for international students (including Korean) and am now an airline pilot. Though I don't have much experience with international operations, what I saw as an instructor is freshly minted pilots going back to their home countries and immediately being put into the right seat of an airliner. Many of these students were very poor pilots, however, as long as they have the money, the flight training machine that exists in states like Florida will keep training them, and international airlines will continue to hire the product. It's a matter of national pride for many countries to be able to employ their own citizens as pilots. Many will cease learning as soon as they leave flight school due to the poor training environments that exist in some places.

Going from a small prop plane to an airliner is perfectly acceptable. It's been going on for a long time and can produce safe pilots, but those pilots need to understand basic stick and rudder flying and continue to hone their skills. Unfortunately, many get started using the automation and allow their flying skills to atrophy. This is true for long-time airline pilots as well.

In the US, by the time a pilot has reached the cockpit of something like a 777, they've gained quite a bit of experience flying smaller prop planes and regional jets, which require a little more work on the part of the pilot. The visual approach assigned to Asiana Flight 214 is a non-issue to US airlines. It's a routine, every day occurrence that doesn't cause one to become "very concerned", however, many countries choose to focus their pilot training more on managing automation than flying the aircraft, and I think that cultural difference played a big part in this crash.

Talk to a US airline pilot who has worked with a training department internationally. The stories you'll hear are pretty eye opening.