I've participated in a couple of offshored large application maintenance projects - from the "other" side, and must say that in general processes are the same, except everything takes more time.
Most critical traps I have experienced are:
- Communication issues (if you take over existing application, have to learn existing "local" slang, probably learn new business area - takes time ~3 months, also English is different in different countries)
- Politics (employees who are loosing their jobs do not make it easier for knowledge transfer, and legacy systems are rarely documented)
- Production problems (while there is "parallel run", call center calls old employees anyway, offshoring guys get hardly involved - thus there is lack of experience
The only effective way how to combat these issues is having extensive staff onsite during knowledge transfer period (~1/2year), and small number of people later on, who are handling communication, but are not managers, i.e., can do fixes themselves, if necessary