Plot hole: An important plot point (in the book and the film) is that Charles Calthrop - thought to be the Jackal, at that stage - played some mysterious part in the 1961 assassination of Rafael Trujillo, the dictator of The Dominican Republic, and rumours of his involvement came to the attention of MI6 and Special Branch, leading to the accidental exposure of the Jackal's false passport. In fact there is no mystery at all about the assassination of Trujillo and there were no shadowy foreigners involved. It was organised by Trujillo's own senior aides, amongst them General Juan Tomás Díaz, Antonio de la Maza, Amado Garcia Guerroro and General Antonio Imbert Barrera. The gunman was later identified as Luis Aniama Tio. All the conspirators except Tio were arrested, tortured, and shot. There was no panicked evacuation of foreigners who were involved with Trujillo's regime, and no reason for them to be concerned - the government did not fall and Trujillo's brother Hector took over as President, ruling in a brutal and totalitarian manner for a further eight years. Any rumours of a mysterious Englishman would have been dismissed out of hand and would not have made it onto even the lowest level filing system anywhere in Whitehall.
Plot hole: Swapping his dental X-ray records with his deceased partner won't convince anyone that Varrick is dead - then (as now) the patient's name appears on the X-ray.
Plot hole: Sergeant Howie is expected to report back to the mainland on the same day he left, and since he took a valuable aircraft with him on his trip it is inconceivable that his superior officers would not come looking for him if he didn't show up. First they would try contacting him on his radio and not receiving a reply they'd send out a search party, and they would do so within twenty four hours. Missing police officers are taken very, very seriously indeed.
Plot hole: Why would a timer be used on a booby trap in the mail box, only that it serves later on to kill Briggs?
Suggested correction: As a back up detonator.
Plot hole: The Emir wants to test Shaft's ability to resist the desert, since he'll have to cross it in his trip, and so sets him up for a test; a room filled with sand, burning hot from dozens of lamps on the ceiling, that heat it all up to 110F. And they want him to walk for 8 hours in that room. But Shaft finds another solution; he digs a hole in the sand and lies in it. Which impresses the Emir greatly, so he shuts off the lamps and tells him he passed the test. How in the world digging a shallow bed and lying down in burning hot sand, with his head sticking out fully exposed, is any indication of being able to cross the desert, let alone survive it for 8 hours? He would have gotten a terrible sunburn with his head exposed as his body cooks in a sauna, and he is not an inch closer to getting to the other side of the imaginary desert.