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: Doyle attends Gondorff's betting shop three times, and he listens to the announcer calling three races from three different race tracks - Narragansett in Rhode Island, Belmont in New York, and Riverside Park in Missouri. He cannot possibly miss the fact that the same announcer calls all three races! J.J. Singleton, the race caller, has an instantly recognisable voice, and Doyle wouldn't be fooled for a second. Each race track would have had its own announcer.
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: James Bond shouldn't have gotten away at the end of the airport scene, where he steals an aeroplane and pretends to be a flying instructor. He had no wings with which to fly away, and he ended back up right outside the airport. So, the henchmen, who seemed to still be chasing him one shot before he parked, should have been right on him, waiting when he got out of the plane.
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.
Suggested correction: There are a lot of things Doyle is processing when he's in the shop. There's a lot happening, and he has a lot on his mind, and increasing pressure and stress each time. It's quite possible that he wouldn't notice the accent of the announcer, something he has no reason to doubt.
Rubbish. During his first two visits, he sits quietly listening to the race announcements. On his second visit, he would recognize J.J. Singleton's distinctive voice and would realize something was very wrong.