While the boat is supposedly anchored at a deserted island, Tinker (Billy Sands) comes up from the engine bay, to tell McHale that the engines are operational again. Behind Tinker, the open sea can be seen, and the boat is apparently moving, as evidenced by the wake.
While Charlie's plane is on the ground, before Mr. Parker takes off, it's wings, elevators, and tail rudder all have rounded ends, and it has a two-man cockpit. But, during Parker's erratic flight, the plane is clearly different, in that it's wings, elevators and tail rudder all have square ends, and it has a one-man cockpit.
In the end, the Congresswoman chooses the PT 109 for the War Bond Tour, whose Commander, of course, is Lieutenant John F. Kennedy.
Parker says that he lives in Schenectady, New York. Later episodes will establish that he was born in Ohio--the same state where actor Tim Conway was born.