The castaways or at least Gilligan would have seen and heard the space camera landing.
The pot of boiling glue would not have exploded unless the cover was fastened down and sealed. The cover was loose and being moved around by pressure escaping in small bursts.
A lens falling off a camera wouldn't necessarily cause the picture on the other end to be totally lost. Just blurry. Furthermore, The Professor could've found a way to repair the camera after it broke when Gilligan accidentally tripped over the tripod getting the signs.
When the castaways chase Gilligan into the supply hut and the pile of feathers after the glue pot exploded, some of them (most notably Mary Ann) are just throwing feathers at one another.
As the Professor, Gilligan and the Skipper first examine the Mars probe, a large modern building is visible behind Gilligan's head (in the distance) on their uncharted and deserted island.
The Professor's big pot of glue is much too large to glue the pieces of a small lens back together.
The castaways seemed to suffer no burns or other ill effects from being covered with boiling glue.
After the Mars probe lands and is sitting on the island's beach, as flames are coming out of the bottom of the probe, you can see the flare that created the flames fall out of the bottom into the sand.
It is ridiculous to believe that NASA scientists could see pictures of the castaway's island and think that it is Mars.