After the helicopter crashes, Hurley appears to be wearing a life vest while taking Aaron to the life raft, but after a moment the life vest disappears.
When Desmond is pulled from the water onto the lifeboat after the helicopter crashes, he is barefoot. However, when he climbs onto Penny's boat a few scenes later, he is wearing sneakers.
When Ben falls from the stairs in the Orchid Station and cuts his arm, his crowbar falls down next to the wall. In the next shot, the crowbar lies in front of him.
As far as the world knew, the plane had been recovered and all the bodies were accounted for. No one knew that it was a fake wreckage. Yet, no one questioned how the Oceanic Six miraculously turned up alive after their bodies had supposedly been found.
As Kate was in custody when she boarded the flight, the authorities would know that she wasn't pregnant. Yet she is able to pass Aaron off as hers and no one bats an eyelid.