When Dr. Balinkoff reveals his master plan to the castaways, he pronounces the location of the heist as Fort K-nox, but later in the story, gives the proper pronunciation with a silent K.
When Balinkoff shows Gilligan the control computer, it is off, but Gilligan is under control. A moment later, it is on.
Controlling humans with magic rings is scientifically unfeasible.
In "The Friendly Physician" (#2.29), Balinkoff took the castaways to his island, transposed their minds and they ultimately freed themselves and transposed Balinkoff into a cat (and vice versa) and Igor (seen here as a monkey) into a dog (and vice versa) before leaving for their island. Months later, Balinkoff has gotten back to human form.
No one seems to find it the least bit strange that Gilligan finds an expensive ring in the jungle which none of them know anything about.
Dr. Balinkoff made his first appearance in #2.29 The Friendly Physician, when he took the castaways to his island. At the end of that episode, Balinkoff & Igor have their minds accidentally transferred into a cat (Balinkoff) & a dog (Igor). Now, the Dr. is back in human form & Igor is monkey & not transformed back to human form, but with no explanation how this happened.
Dr. Balinkoff does an abrupt about face in his attitude about money. In his last appearance, when Howell tried to bribe him by offering millions of dollars, Balinkoff just sneered. But now, he plans on stealing all the gold in Fort Knox.