My father told me of a story that while he was young working at an electronics company, they all signed a disc that was shrunk down and mounted to one of the lunar rovers. Does anyone know anything about this?
This actually is a very common practice among space hardware. Evidence is seen today in things like "Send your name to Mars" for the general public. Most space missions I'm aware of try to do something like this, put the signatures of the people who made it with the object on some obscure part, a disc usually. These private discs are rarely spoken of in public, and would thus make discovery of them rather difficult. You'd have to find someone who personally worked with the rover and ask them.
Bottom line, I would believe your father, but you're unlikely to find any proof.
I was suspicious at the "shrunk down" part of the story, but then I came across this comment which explains a similar occasion:
My wife's father, Herb Gulbrandsen, (deceased) worked on the LEM. Along with what we make out to be about 200 other people, he signed a picture of the craft. In the right hand corner of this pic is a cloverleaf logo with Grumman/NASA/Lunar Module respectively placed on each "petal" of the leaf. At the bottom right is a description of the craft and when it was shipped - October 10/15 1968. A copy of this was put on a piece of microfilm (Mrs. Gulbrandsen's description) and placed on the Apollo 11 lander. Many of the signatures are fairly legible, including Herb Gulbrandsen's off to the left of the right hand leg pad.
Which sounds plausible enough, a microfiche would be easy to stash somewhere on the LEM (officially or not).
History Detectives on PBS did a show about this. You will see it there if you look on video.pbs.org.
They were looking for rumors of Andy Warhol art going to the moon. I believe this is what your dad was referring to.