The problems, according to the article, involve delays, missing paperwork, and less-than-helpful U.S. embassy staff. They appear to be more serious for visitors from China, India, the Middle East, and Russia. A postdoc in genetics at MIT, from Belarus, ran into 3 months of bureaucratic delays and lost documents when she tried to renew her visa with the U.S. embassy in Minsk on a visit home. She ended up having to go to Moscow to get the visa.
An anonymous State Department source told the Times that delays like these (2-3 months) are common and a result of "an unfortunate staffing shortage." The Belarus postdoc, by the way, has decided not to do further work in the U.S.
The international student director at MIT says the problems often occur when the students or postdocs leave the U.S., for brief visits home or to attend scientific meetings. Trying to get a visa to return is when the problems often begin.
Visa procedures tightened markedly after the 11 September 2001 attacks but in recent years, the U.S. government improved the procedures that cut delays to about two weeks, and students began returning. In the 2007/2008 academic year, according to the Open Doors survey by International Institute of Education, the number of international students on U.S. campuses jumped 7% over 2006/2007. And the 2006/2007 year itself showed a 3% gain over 2005/2006. The Open Doors surveys also show that life science, physical science, computer science, engineering, and mathematics account for more than one-third (34.5%) of foreign students in the United States.
The problems, according to the article, caused AAAS (publisher of this blog and Science magazine) to convene a meeting with the National Academy of Sciences and several dozen other science organizations, to bring those problems to the attention of the State Department. As the MIT international student director told the Times, "There are other countries that want these folks. They are the best of the best. They have other options."
Update: The Times story reminds us of a 2004 account in Science Careers of Haitham Idriss, a Thomas Jefferson University postdoc who went to Canada one weekend for some R&R. When he tried to reenter the United States, he was told he needed to register for a program called NSEERS, the provisions of which he found onerous. He refused and was not readmited. Outside the U.S., he never found another scientific position.
The last time we spoke to Idriss, we learned that he had given up on research and started a new scientific journal, Annals of Alquds Medicine, which now seems to be defunct. It was a pretty standard journal in all but two respects: it didn't allow submissions from an Israeli address, and it didn't allow references to evolution--which, Idriss maintained, contradicted Islamic orthodoxy. Make of this what you will.