Boyd,
I have had CAD drawings, mechanical engineering work, general research, and business logos done through elance and odesk. My experiences have been positive. A couple thoughts:
1. A Good Write Up - Some of the $ savings will be traded for your time. You will need to spend time thinking through, and then very clearly writing, what it is you want. Some people on elance and odesk communicate via phone and skype but otherwise it will be email. Can someone unfamiliar with your project, do exactly what you want with your written description? Sending your write-up to a friend or colleague who doesn't know about your project might be a way to start.
2. Trial Run - It depends on the work you need done, but I have friends who use elance and odesk daily and before they move with a big project, they have people bid on and complete a small, sometimes fake/useless project. It is 'real' work for the people bidding, and they get paid for the work, it just doesn't really matter to my friends. This lets them see people's work ethic and style on something cheap that doesn't matter before they say go on the bigger project.
3. Building Codes - My work requests didn't have to meet any regulations, but yours will. You will need to ensure those parameters are being met. This might mean U.S. only vendors. You can specify that fact, but it does limit who responds and raises that rates.
For me, my experiences have been totally positive and also, not to get sappy, really heartwarming. I think it is so cool that people around the world are hard-working, honest, creative, and want to bid on projects.
Good luck, Brett