Continuity mistake: When Frost is checking the documents at the Counterfeiters house, Frost borrows his glasses and in a quick camera shot of the Counterfeiter he is wearing them even though he has passed them to Frost.
Factual error: The station under Cape Town stadium do not exist. Although the first tram line was from Cape Town to Green Point (the stadium's location) it was discontinued just before world war 2.
Plot hole: When the CIA detects that Matt is accessing sensitive information to track Frost, they trace Matt's location and find out that he is using a public computer in a cafe. We then see that Matt is viewing the same kind of software, files, etc. that the CIA views at their agency. There is simply no plausible way that a random public computer would have CIA software, or be able to access CIA data at all, regardless of Matt's clearance. The computer itself would have to be on a secure domain.
Continuity mistake: When the agents fly over from DC to Cape Town in the private jet, the in-flight exterior shot shows the plane as a Falcon, yet when it lands it is a Gulfstream.
Other mistake: Twice during the film the words "C.I.A Headquarters." appears in the bottom of the screen. This is a grammatical mistake as the filmmakers forgot the third period/dot after the "A" in "C.I.A."
Continuity mistake: When Denzel is at the forger's house, they are upstairs drinking wine. They toast and Denzel drains his wine glass. The shot changes to show both characters and Denzel is seen to place his now half-full glass of wine on the table. No time has passed to refill his glass.