In the beginning Rydal recounts the legend of Aegeus on the steps of the Acropolis and says that it was there that Aegeus jumped to his death after his son, Theseus returned from Crete and forgot to change the black sails to white to denote his success. This is untrue; you would not be able to see the Aegean from the Acropolis, anyway. According to the legend Aegeus was waiting for the ships to arrive at Cape Sounion and when he saw the black sails he plunged into the sea (which is called the Aegean Sea after him). It is unlikely that a tour guide would not know how to recount the legend properly.
When Chester asks the detective if he was a Marine, the detective says "Yes" and that he was happy when he left Europe after the war. Although some believe the Marines were not in Europe during World War II, there were several units deployed there for security and guard duty (the US Embassy in London being one example), and to support Operation Overlord (the invasion at Normandy). They were also used by the OSS, the Office of Strategic Services, for covert missions in Europe during the war. Thus the detective could have easily seen service in Europe during the war.
Before entering the ruins, it is supposedly dark, and rainy. The shadows on the ground however tell another story. The sharp shadows suggests the scene is in broad daylight, and is just darkened to suggest the sudden thunderstorm.
When Rydal is talking to Chester at the beach in the evening, there is a wisp of hair in the middle of his forehead. A moment later when his face is shown again it is a full flock of hair over his right eye.
Colette's driver's license has her date of birth (4/12/59) with her age being 31. But the date of issue is 12/12/59, which would make her 28 at the time. 31 is her age when the movie takes place.
When Chester lands in Istanbul , camera flies over ever famous Galata Bridge as it is now in present instead of narrow two lane bridge in 1962.
Chester sits on a plane in 1962 (as evidenced by the date on a gravestone). However, the De Haviland Comet with square windows as seen in the film was discontinued years before. The improved Comet 2 and the prototype Comet 3 culminated in the redesigned Comet 4 series which debuted in 1958.
The restaurant on the sea where the three of them go after having arrived in Iraklion from Athens, is actually in Xania city limits. It's "Thalassino Ageri" in the dismissed tobacco manufacturing area . They went there because no hotel in Iraklion wanted to host them and they spent the night there waiting for the bus to Xania due the following morning.