I've been living outside the U.S. since 1994 and have never had any problems regarding my residence and working outages.
For background checks and security clearances, how long between outages is more important than where you live. If you've been out of the business for more than 6 months or a year then you may be subject to more paperwork and a longer waiting time to get your clearance done. Best thing is to be prepared with a printed list of contacts and references who you know will answer the phone during business hours. You may even be able to get some of the paperwork faxed or mailed to you if you are confirming early enough. Bartlett has done that a few times, for example.
As far as unemployment, I can only say that the last state I actually resided in (Ohio) told me I could not collect unemployment if I was living outside the U.S. or its' territories (USVI, Guam, etc). I've never pursued it any further since I've always worked between outages anyways. (Taught scuba in the Cayman Islands for 7 years and currently work as an English trainer and business English consultant in Vienna.) Of course, this brings up the whole foreign earned income and legal residence and where do you file from questions.
The biggest things (I think) to consider are your travel methods, time and expenses. Some places have a cap on travel that may not cover the air fare. Is it better to keep a car in the U.S. or rent? Speaking of driving, will you be able to keep renewing your driving license in the U.S. ? Will you be able to get a license in your new country of residence? Can you use your U.S. license to drive in your new country of residence? Where will you be keeping and spending your money. For example, I would take a HUGE hit right now if I worked an outage and wanted to bring the cash back with 1 Euro costing about $1.28 right now. So for now what I earn in the U.S. stays there.
Anyways, these are just some of the questions I've had to answer for myself over the years. Luckily, they are all pretty easy to answer, given the internet and instant access to information.
Hope this was more help than it was boring. If you have any specific questions I'l be glad to try and help.