I left my passport in my jeans pocket to wash. The passport is not damaged but the stamps are gone. I'm in Korea and the stamp mark from my arrival can be barely seen. Will it be a problem going through the custom?
Personally I would visit the Immigration office (or at least call) and talk to them about the issue. They may not care, they may want to re-stamp your passport or something else. But better to resolve this now, rather than risk missing your flight because of delays while they deal with it at departure.
Even if your country is ok with it (or the country of visit), the airline can stop you from travelling if they considered your passport to be damaged.
Just today, there was an article about Jetstar barring a passenger from travelling with a tattered passport.
The passenger had confirmed with the embassy that his passport was ok, but it's also up to the airline to confirm that it meets the standards.