I read through all the answers and i think all have their share in explaining individual benefits or shortcomings of outsourcing production.
Let me try a more general approach: Outsourcing is nothing else but the attempt of a producing economic entity to become more competitive. This can be a company who tries to concentrate on core competences - thus outsourcing the cleaning of building windows or mowing the lawn to external service companies. It can also be the desire of an entire economy and its policy to take advantage of low cost countries (as happens with the US).
But here things get complicated. If an economy outsources more of its producing industry than the technological progress allows, then this will lead to importing products more than exporting. You may ask: so what? But the idea is that you can only trade storable products, goods, you can´t trade services. At the end this creates trade imbalances and current account distortions.
Whatever we think of the world economic situation, most problems and hickups can be traced back to these imbalances.
Ousourcing is like medication that is beneficial in small and well applied portions. Like any drug, if you overdose, it will hurt you.