Before take-off, the close-up of Pagnolini sitting in the helicopter shows a US Coast Guard building just behind the helicopter, but the aerial shot shows there are no buildings nearby.
When Pagnolini's helicopter is flying over the speedboat, the long shot of the boat shows that it is travelling slowly but the close-up shows that it is travelling very fast with a considerable wake behind it.
The SOS sent by the Requoit is wrong. It's depicted as one dash followed by three dots. An SOS is actually three dots, three dashes, and three dots. However, while the code isn't an SOS, there's no reason the boat couldn't be transmitting an incorrect SOS, especially considering there's quite a lot of evidence something supernatural is occurring. The nonstop repeating "dash dot dot dot" the boat is transmitting would still be interpreted as a distress signal.
The air-sea rescue helicopter shown in the film actually had a crew of three, not two as shown in the film: there had to be a winch operator to lower the medic and the rescue basket while the pilot controlled the aircraft.
The pilot's haircut is not even close to regulation.
As previously stated, these USCG rescue helicopters never had crews of only two people. Furthermore, the personnel who perform the rescue are medically trained rescue personnel, it is an intense special training. They and the pilots would have a familiarity of each other's job / training, but would never be completely cross trained. The military would consider that a waste of training expense.
When Kim Novak is retelling her story and confesses to the priest about being a prostitute, he states, "So was Mary Magdalene."
In 1969, six years before this movie was released, Pope Paul VI issued an official Papal decree removing the identification of prostitute with that of the "sinful woman" who is known as Mary of Bethany. A Catholic priest would have known this and not used the reference.
When Lt.Pagnolini uses a megaphone at the beginning, you can hear reverberation, which is impossible on the sea.
When Pagnolini's helicopter is flying over the lighthouse, the shadows on the ground show that the helicopter is flying in an east to west direction when, as they are supposed to be operating out of Miami, they should be travelling west to east.