I'm planning to travel to the Philippines next month with a travel document duly issued by the Philippine Consulate, Los Angeles as my passport had expired a few months ago. Do I get concerned while in transit in South Korea with only a travel document?
Not really, a friend of mine had his Sri Lankan passport stolen near Anaheim, Los Angeles a few months back. He also had to return with a temporary travel document issued by the SL embassy in LA. He transited in Doha and said everything went fine, except they looked at you like you were deported from the US. :) I don't know about Seoul, but I doubt you should have anything to worry as long as the document is valid.
Again I'm not familiar with the particulars of your country, but Sri Lankans can renew their expired passports overseas. I guess many countries have this facility. Check that out too. My friend had to come back to get the US visa stamped again.
You should call the airport airline representative and check with them since there are airlines that does not allow travel documents. Philippine Airline for sure will allow travel documents since they fly direct to the Philippines.