Moe and Homer cover their mouths to hide lip movement because, obviously, when this episode was produced, they had no idea who would be playing in the Super Bowl, but could dub in the team names after the NFC and AFC championship games. The additional joke of hiding their mouths when naming the president and his wife is due to the national crisis when Bill Clinton was impeached by the House of Representatives in 1998 for perjury and obstruction of justice. The events leading to his impeachment first made news in January 1998 and proceeded throughout the year when this episode was in production.
Steven Dean Moore made Rupert Murdoch do several takes of his line, "I'm Rupert Murdoch, the billionaire tyrant," as he found the line extremely funny.
The version uploaded to Disney+ modifies the Catholic Church commercial. It no longer says, "The Catholic Church. We've made a few changes." It removes "Catholic" and simply says, "The Church. We've made a few changes."
The Super Bowl commercial for the Catholic Church that Marge and Lisa watch was inspired by real-life Super Bowl commercials in which, according to Mike Scully, "you don't know what the product is" because there is "so much going on" in Super Bowl commercials. It was also based on ZZ Top: Legs (1984). Although they had come up with the commercial's premise, they were not sure of what its tagline would be. Eventually, Tom Martin suggested "The Catholic Church... we've made a few changes." It got the biggest laugh from the other writers and was subsequently included in the episode.
On the morning of the table read for this episode, Simpsons writer George Meyer heard on the radio that Phil Hartman had been murdered by his wife. When he told executive producer Mike Scully what happened, Scully informed the rest of the crew, and the table read was canceled for that day.