Migration can only be a bad thing for developing nations. Their most talented and gifted citizens leave the country in search of better paid and more rewarding jobs in developed nations and therefore leave a only the less talented behind. This means a lower quality of provision in these professions in their home country, meaning that the nation as a whole cannot develop further.
Migration leads to loss of talented people because they start living abroad and all their talent is utilized by already developed nations. Migration provides no opportunity for a developing country to grow any further. It delays the process of development to a great extent and closes various venues of growth.
Immigration into developing nations can be very beneficial if the right people immigrate into the country an can fill the holes in the nation's skill pool, knowledge base, or economic resource pools. If the immigrants do not fill the particular needs of the nation, then it just brings more bodies in to split up the resources. There are a lot of people who move to nations that are beginning to develop because there are often jobs for them that cannot be filled by locals because the locals do not have the required training.
It kind of depends on where in the development cycle the nation is. At the very beginning of an industry in a region, there is a skill deficit because there are very few who have done the job, and very often no training programs. (There has to be a certain level of local demand in computer networking, for example, before students are likely to sign up for networking classes at the local universities, or even before there are people qualified to teach the courses.) Thus immigration is often very important in the beginning stages of the development of particular industries.
On the other hand, emigration from these nations of people with required skill sets, or monetary/intellectual capital can be detrimental to the rate of development. By the same token, emigration of people who cannot or do not contribute to the nation's development can be beneficial because there are fewer people among whom to split the resources (natural, economic, educational, political). This includes political dissidents who might otherwise use political power to work against the development of key industries.
Migration is simply the movement of people and it does not hurt developing nations. Migration actually goes hand in hand with development because development brings more money and more jobs. People relocate for better opportunities or better resources. I think migration does more to help development, rather than hinder it.
Migration is not bad for developing nations. The fact that people are willing come to a country, bringing their family and professional skills is great for the economy of a developing country. It allows the developing country to gain the diversity that is required to be an effective member of the global marketplace.