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Digital Fortress - 7 mistakes
Continuity: In Chapter 120, the main characters discover what they realize is an 8-by-8 Caesar box code. The first two times we see the letters of this code, the fourth sequence of four letters reads MFHA. The first letter, M, is a typo - it should actually be P. When the letters are grouped in an 8-by-8 grid in Chapter 121, this sequence has now changed to the correct PFHA. The correct letter P gives you the word "responsible"; the incorrect letter M would yield "resmonsible".
Plot hole: Early on in the book the NSA is described as a top secret agency, an agency very few Americans know exist. However throughout the rest of the book there are many references to groups who openly protest against the NSA, bad widespread publicity, and the majority of Americans being against the agency. If hardly anybody knows about the NSA then how can there be so much open debate about it?