For Thailand. check the website
Thailand news, forum, visa, immigration : thaivisa.com for info about obtaining a work permit, but as already said, life is much easier as an Instructor. On the west coast of Thailand, esp Koh Lanta and Koh Phi Phi, foreign DMs are used. Whether or not they are legal can be a different story tho'. In Thailand there are relatively few local DMs, but in the Philippines and Indo for example, the opposite is the case...
I wouldn't worry too much about people saying you can't find work if you only speak English too - this is a fallacy. I am English and have never, in over ten years, had a problem finding work. You just need to put the right spin on it. Dive centres need languages, sure, but beng a native English speaker is a huge plus too. For example a French instructor would be able to teach in French, and maybe in English, but a native English speaker will be able to communicate better with a wider variety of nationalities. We can communicate and explain things better to people who take the course in English, when English is their second language. And a huge percentage of students in Asia fall into this category. Speaking a second language is a great skill to have, but so is being a native English speaker...
And also ignore the dive centre owners who discard a CV because it says you were trained in Thailand. It's probably not a good idea to work for someone so narrow-minded. If they can't be bothered to judge you as an individual, then look elsewhere. As if all instructors in Thailand are bad ? Thailand just has a huge dive industry, so anyone with the nous to understand the basic concept of percentages should be able to work out the stupidity of these claims. Thailand has more instructors than it's neighbouring countries, and therefore it will have more good instructors as well as more bad instructors, but the percentages of good and bad wouldn't be different. Location doesn't not make someone a better instructor than another person. Having worked all over the Asia-Pacific region, it seems to come from jealousy. For example, the dive industry in Australia looks down on the Thai industry because Thailand gets way more students. Then you go to New Zealand, and they look down their noses at people trained in Australia for the same reasons...