Gilligan breaks the Fourth Wall when his head is outside the missile & the Professor warns him that if he makes a wrong move while disarming the missile, that he could blow everyone up.
The location of the island was always a little fuzzy throughout the show. In this episode, the location the Air Force marks on the map is due southeast from Hawaii. In So Sorry, My Island Now (1965) the Skipper instructed Gilligan to drive the submarine due northwest.
A location of 10"N 140"W is consistent with this. (The radio actually said 140 latitude, 10 longitude, which doesn't exist.)
In this episode, it is shown how the radio was able to work for so long in the show. The batteries were rechargeable and the professor developed a scheme to charge them.
The missile that Gilligan goes for a ride in looks nothing like the one in the launch scene.
Mary Ann enjoys listening to a soap opera called "Young Dr. Malone," which had a long run on radio from 1939 to 1960. There was also a television version that ended in 1963.