Other mistake: Samantha is reading a 4-line note from Endora. The paper is semi-transparent and in a shot from the front, we can easily see the writing through the paper. However, after the note is "twitched" into a second, shorter note, there's another shot from the front - and the lettering looks exactly the same as it did before. (00:16:40)
Revealing mistake: When Endora goes to Darrin's workplace and puts the spell on him she appears to be floating. Look closely and you can see the wires holding her up.
Answer: Telstar was an early communications satellite system. Darrin, in a particularly sexist manner reflective of this era, is saying that telling a secret to a woman means it is guaranteed to be "broadcasted" to multiple people.
raywest ★