Chris Koch quotes me and others in CSO magazine around security issues when offshoring. There are several other dimensions around security - given relatively poor physical infrastructure in many offshore locations, badging of on-site employees, secure access to dedicated client areas, information security etc.
There are several other unique due diligence areas - business continuity (often due to geo-political risk), hr standards (ergonomics, visa compliance, health/safety, recruiting/retention, on-site housing, others), telecomm connectivity and robustness, financial stability/standards, intellectual property protection, data privacy protection, methods/tools, key staff interviews and several others.
The good news is many offshore vendors (especially Indian ones) have gone through such diligence from many buyers and come off with flying colors. After 9/11 accented the need for such reviews, a number of CIOs were impressed with redundancies offshore vendors had built into their infrastructure compared to their own operations.
The bad news is instead of proactively developing FAQs for these areas you often have to pry out of the offshore vendors their positioning/capability in many of these areas.