When Sam (Rob Lowe) is given the NSA report, the number and positions of blacked out lines change several times between shots.
When the National Security Advisor shows Sam Gault's file, the cover page is labeled "CONFIDENTIAL," and Sam remarks that he is not cleared for code word clearance information. Code word clearance is used for Secret and above classifications, not Confidential.
The monogram on Sam's pocket is "sNs" (big N). In monograms where the middle letter is biggest, the middle letter is supposed to be the last initial, not the middle one. It should read "sSn" (big S in the middle).
The geographer states the map maker Mercator was German; he was, in fact, Flemish.