A company I worked for briefly in Ireland was getting a company in South Africa to do their drafting. With the exchange rate and the lack of work at the time in SA, it was a win-win situation. In the days of DSL and video conferencing, it's easy to exchange data, scan mark-ups and email them, etc.
Time zones can be a pain or not. Ireland and SA are one hour apart. If you need something today and you're dealing with a CAD tech in India and you're in the US, you may catch him at the end of his work day and you won't get it until the start of your next one. Someone in Australia, on the other hand, you could catch at the end of your work day and the start of theirs. You also have to watch the Middle East work days -- their weekend is Thursday afternoon/Friday, not Sat/Sun.
As far as quality of work goes, I'm sure you'll be pleasantly surprised. Washington Accord countries recognize substantial equivalence with respect to undergraduate degrees and most other countries don't have the "humanities" requirements in an engineering degree, meaning that they do more engineering in their undergraduate degree. PE in the US is usually considered substantially equivalent to Pr.Eng. in South Africa, CEng in the UK, CPEng in Australia, etc.
Their codes will be different and they will probably work in metric not Imperial units, which may be a problem with software and "glaring errors" not being noticed.
I'd stick to a country where English is widely spoken. China may offer cheap, reliable engineering services, but is it worthwhile if you have to carefully copy edit the Engrish on your drawings?