If you aren't a Senator who can call up the head of Homeland Security, or a high-powered nun whose boss who can ring up Karl Rove, working free from government watch lists will be a tedious and not-very transparent process.
The first rule for most people in getting off a watch list is to accept that you are not on a list.
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If your problem is domestic- or international-travel-related, you can try the Department of Homeland Security's new online redress system, called the Traveler Redress Inquiry Program, reintroduced in February. (The old one was so badly designed that Congress opened an investigation). After filling out the form with details, a stymied traveler will need to submit copies of identification documents. You can file online, or submit a version by fax, mail or e-mail.
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If you find you can't get a credit card or a mortgage or an apartment lease, you can get a copy of your credit report from AnnualCreditReport.com (you're entitled to a free copy from each of the three major credit bureaus once a year). Look to see if there is an OFAC (Office of Foreign Assets Control) alert on the report. If there is, and you're not actually on the list -- which is public -- contact the credit bureau, the Fair Trade Commission, advocacy groups and the media. There's no clear legal recourse, but shame can work wonders with big companies.
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If you're on one of the secret government watch lists, the feds say you have to find the agency that nominated you to the list, and appeal through that agency's ombudsman, privacy officer or Inspector General. The Terrorist Screening Center maintains the master "unified terrorist watch list" (which you can't see), but says it is only the keeper, not the creator, of the list. Nevertheless, in 2005 the center removed 31 entries, based on complaints forwarded to it by watch-list-using agencies, according to a recent Congressional report.
More:
http://www.wired.com/politics/onlinerights/news/2007/04/watchlist2