When "Saturday Night Live" hosts and cast members stare into the camera, hoping to utter their lines with perfect comedic timing on live television, they are focused on one thing only: the cardboard cue cards held up by Wally Feresten.

"Wally is a character in every sketch, you just don't see him," says Alec Baldwin, a 16-time SNL host who has also worked with Mr. Feresten on live episodes of "30 Rock."

For...