When Dr Weston makes the pen invisible, he picks it up and writes his name down on a piece of paper. This could not happen, if the entire pen is invisible then the ink would be as well, so you would not see anything. A partial explanation for this is offered later in the episode, when Dan tells Nick Maggio that when he is invisible, anything that he takes into his body (food, drugs, etc.) becomes invisible, while anything that leaves his body (blood) becomes visible.
There is in fact a radio station KLAE on 101.3 in Marshland, Oregon.
In later years, David McCallum considered the feature length pilot to be the only good addition of "The Invisible Man," due to the suspense element. The actor also stated that the more comic approach to the regular show, came as a disappointment to him.
Cast here as the main villain, Jackie Cooper would become better known as Perry White in the "Superman" movies.
If a person were to become invisible he would be blind, as the retina would be invisible, light would pass right through it without any resistance. Without light hitting the retina, the person could not see anything around them.