When the Professor comes back with the radio Mr Howell and Gilligan are in a different position. This should be impossible as they could not release themselves from the mine previously.
A World War II mine does not have enough magnetic force to pull Gilligan and Mr. Howell to it by their jewelry.
Ultra high frequency waves from a transistor radio cannot neutralize magnetic waves.
When Gilligan is trying to row the raft away from the mine, the Skipper is yelling at him to "cut the line" connecting the mine to the raft. This wouldn't do any good, as it was just pointed out that there is a metal rudder on the raft that will attract the mine.
When the mine explodes in the lagoon and showers the castaways with fish, the "big fish" that Gilligan "catches" is obviously a plastic fake.
Just after the part where Gilligan and Mr. Howell are trapped by the mine's magnetic field (and are released), the four men return to the mine. However, Mr. Howell is wearing an obviously metal belt buckle, but not suffering from the magnetic field.
The mine is heavy enough that it took three men to hold it while Gilligan went underneath. If it was that heavy, Gilligan would have never been able to pull it in on land from the water with a fishing pole. Not to mention how did he roll it himself back out into the ocean.
Although the raft appears to be undamaged after Gilligan paddles it up the beach and into the jungle, it's never seen or mentioned again.
When their jewelry causes Gilligan and Mr Howell to be pulled toward the mine, any of the characters should have thought of simply removing the jewelry. But it's completely out of character for the Professor to overlook this obvious solution.