One of the more important ones is monetary policy. In the past few decades, where all of the usually cited examples are taken from, a "strong dollar" policy kept US manufactured goods expensive on the world market, and made imports cheap. Predictably, free trade led to the long, grinding destruction of our manufacturing base.
Currently the policies are much more moderate and favorable to US manufacturing, and what we have (with surprisingly little fanfare) is an export boom -
http://www.nytimes.com/2011/09/09/business/economy/us-exports-rise-to-record-as-trade-deficit-shrinks.html. So all year US exports have been setting new records. You still hear laments of "we don't make anything here anymore", but times change, and good policies can bring good results.
Another factor is the character of the trade; Columbia and Panama have little but agricultural products to sell, basically stuff that we can't grow here. We import it already, and it doesn't cost jobs.
South Korea is a modern country like our own - they have a similar standard of living, an excellent education system, and a highly successful socialized healthcare. Its not a matter of competing with child labor, or slave labor. I think the prospect is for a much more healthy and equitable partnership than we have with China, for instance.
Overall I think the knee-jerk reaction against free trade may be well-informed by historic precedents, but nevertheless misguided; the current proposals are likely to do just what the president hopes they will do - and give another small push in the right direction to our economy.