It's actually worth a little typing to metion some hazards associated with non-DoD, DoS, UN, staffing agency work. This isn't going to apply to a guy going over to fly a DC-9 on contract, someone working for Shell Oil or Julius Berger, or someone flying ISR. This will be more pertinent to someone who's contracted to fly some goon's King Air, Hawker, Casa, BAC 1-11, etc.
If you're working for a small US outfit that marries itself to a small, foreign entitiy, you run a good chance of becoming utterly dependent on your own wits to keep yourself and your crew out of harm's way. You therefore need to avoid risk to the best of your ability and educate yourself thoroughly. This way, when you do have to start getting creative, you're taking calculated risks rather than blindly walking into hazards. Conditions from site to site vary so much, that I can't describe specific threats for all locales. That said, there are a few things you're going to want to do.
Basically, decent logistic support will remove many of the risks for the crew and aircraft in the field.
'Til you've been in the country for a while (at least a month or two), you'll really want to limit your travels to the hotel, airport and other places your local contacts can provide escort and security. Don't go out alone and unnoticed. If this sounds boring, it is. Pretend you're flying from an aircraft carrier in the sand/jungle/savannah. This is what you're paid to do.
If and when your logistic chain fails, things get interesting. Changing money, going to banks, walking around certain markets unescorted and using public transit can be really dodgy in certain spots. Handling finances was/is, by far, the most challenging situation I face abroad. It's extremely easy to find yourself getting attention from local thugs (uniformed or non-unifromed) when everyone sees a white guy at a bank. The same goes for how you carry your documents, etc. Your local contact should be able to take care of these tasks for you. If you find yourself in a position that requires you to hit banks to keep your operation running, you are already in a compromised situation.
Again, Kalitta crews, NetJets Europe guys and ISR pilots aren't going to run into this.
Use your local contacts and support to your best advantage.
Also, a lot of governments provide increased security in areas that have lots of expats spending their payrolls. If you can, confine yourself to expat-friendly areas 'til you're intimately familiar with local conditions, politics, etc. Even then, you save no money by leaving expat-friendly areas to get an extra 2% savings. If you're operation insists on doing this, don't be dumb like me. Start looking for another job.
So let's say you're supporting some airplane that has been deployed without enough support. We'll also say that your local contact is no longer friendly. So you now have no transAtlantic cash flow, no secure transportation, no escort and increasing hurdles to day-to-day operations. You'll also be in a position where your operational cash reserves will be rapidly dwindling. You have a very limited amount of time to get logistics figured out or evacuate the site.
Know how to get past certain entities, and get your flight plans into the system independent of handlers. Quietly form a relationship with your own, hand-picked handler and start paying him well. This has to be someone who's not afraid of your local contact. When the locals get angry, they'll use their government contacts and handlers to ensure your airplane doesn't move when it needs to. Preempt this when you see conditions degrading, and you'll be able to get your crew out without abandoning your airframe. This is a dangerous game to play. Again, you need to be thoroughly educated so as not to cross an unwritten line. It sounds all fun and exciting as I type about it, but it's a sweaty pain in the neck when you're in-country.
If you have to travel over land, travel by daylight, and make sure someone knows where you're going and when you should make it there. Nobody in your crew should be leaving the hotel/base/compound without support and some sort of itinerary left for others to track. Guys who are new into the country, especially those who have been abroad in less challenging spots will balk at this. Let the US/UK Embassies in your country know what you're up to.
So let's say you're working for a good operator on a good contract. You should have no reason to open yourself up to local risks. Why worry?
You should still take measures to educate yourself, your crew. Sitting in your hotel room, after dowing a beer at the hotel bar, consider your contingency plans. Things go sour in a matter of 12 hours. Don't blindly trust the repuation of your employer simply because they've been running Hawkers or King Airs in the US for years. If you wind up not using your contingecny plans, and you feel like a geek after the fact, oh well. This is better than trying to figure things out when the chips are down.
How are you going to move funds to make sure you have enough cash available to cover your fuel back to your base?
Can you extract your crew and your airplane from your current location if the local bigwig decides to throw up obstacles to your departure?
What leverage do you, as a site manager/captain/cremember have to ensure that your customer adheres to the terms of his contract? How can this leverage be utilized? Can it be used without damaging the operation or is it only useful as a last resort?
What happens if one of your guys or you gets sick? Do you have copies of your evac. insurance available? Is this paid-up? Do you have copies of overseas health insurance? Don't trust your employer's word. Get documentation.
How much local pull does your customer have? If he gets pissed can he influence key personnel? Has he, in the past, been able to successfully bully airlines into keeping his crews stranded in country?
Can you arrange a safe overland evacuation for your guys, if things go really bad?
How much emergency cash will it take to get all your people out of the country under the worst conditions? How much emergency cash will it take to get all your people and your airplane out of the country under the worst conditions? Acquire these funds (legitimately) and do not touch them 'til you're back in the West at the end of your contract.
Again, you can find your support cut-off overnight, and you don't want to be figuring out the basics when things are hitting the fan.