On the first night of the cruise, Bette Davis's character says good night to Poirot, and he answers "Bonjour". No Belgian, especially one as fastidious and serious as Poirot, who does not play around or joke, would say "Bonjour" for "good night". He would have said "Bon soir," (good night), which he does say to the others as they go.
When Simon and Linette are climbing up the pyramid there's a shot of them having climbed more than half way up, but in the next shot, looking down on them, the ground and rubble is visible only a few meters beneath.
After Linnet Ridgeway is almost crushed by a stone falling down from the temple of Karnak in Luxor, Dr. Bessner advises her to go back to the boat to have a rest. She replies that she must see the temple of Abu Simbel in the evening. In the next scene, she is visiting Abu Simbel with Simon, and in the late evening they are back on the Nile steamer. The problem is that the distance between the temple of Karnak and the temple of Abu Simbel is about 250 miles. The movie is set in the 1930s, when air travel was still primitive, so it's unlikely they flew down there and back in an afternoon. It is definitely impossible for a steamer to travel that distance in one afternoon.
Doctor Bessner identifies the statue on the left of the temple of Abu Simbel as "the singer". He says it's making a howling sound every evening. Both facts are wrong, "the singer" is one of the statues in Thebe West near Luxor of the now destroyed temple of Amenophis III., and it is said that it was "singing" only in the morning hours.
Right after Ms Otterbourne was shot, the murderer dropped the weapon and fled the scene, leaving the gun lying on the floor. And when Poirot and Colonel Race rushed out of the room and saw the gun, Colonel Race picked it up and held it by the barrel. In fact, when a gun has just been fired, its barrel would be too hot to even touch, let alone hold up in the air in one's hands.
The goof items below may give away important plot points.
When Mrs Otterbourne is about to tell Poirot and Colonel Race who cut Louise Bourget's throat, she says "I saw that it was.." and then gets shot. Later on when Poirot solves the murder and we see this scene replayed from outside the window, Mrs Otterbourne says "I saw it.." and then gets shot.
When laying out the sequence of events, Poirot explains that the murderer took out the empty cartridge from the gun and replaced it with a full one so that in the event of the gun being found, only two bullets would appear to have been fired which corroborates the shootings. However, the gun is bundled together with the shawl and the ink-stained napkin, both of which contradict the two shot theory.