Here is the latest from AOPA,
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Background checks now required for some foreign pilot certificate applicants
July 26 — AOPA has learned that FAA field offices will receive on Monday new procedures requiring all foreign pilots to submit to background checks before the agency will issue a U.S. pilot certificate based on a pilot license issued by another country. This new procedure will remove an emergency suspension of pilot certificate issuance to foreign pilots put into place a little over a week ago because of national security concerns.
The policy will establish new procedures for FAR Part 61.75, issuance of an FAA pilot certificate based on a current foreign pilot certificate. Non-U.S. pilots will be required to submit an application directly to the FAA's office in Oklahoma City and, upon approval, will be directed to the appropriate FAA flight standards district office to receive the U.S. certificate. According to the FAA, the entire process could take up to 60 days.
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What this will probably entail is that you get a letter of good character from your local police station and send it with the application. The reason I feel this will be the case is that this letter is what constitutes a background check for the Green card.
It is not too onerous a requirement but keep in mind that previous minor offences may be a problem, public disorder or drunk driving for instance may get you refused.
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