Marcy says the spoof sitcom was canceled because "a housewife in Michigan didn't like it." This is a thinly-veiled jab at Michigan housewife Terry Rakolta, who was offended by "Married with Children" and complained about it on various talk shows. Her efforts to get the show canceled had the opposite effect: More people tuned in, which actually boosted the show's ratings and contributed to its longevity.
The producer of "Pease in a Pod" is named Ron Michaels. The name is a combination of the first names of "MWC" creators/producers Ron Leavitt and Michael G. Moye.
While the Bundys are watching FOX, multiple promos and announcements promote "NFL on FOX"--with emphasis on FOX. This is making fun of The FOX network's heavy promotion of its NFL on FOX programming in real life, which came to the network for the first time in the 1994-1995 season. The next episode in this season, "Dud Bowl", and several others throughout the next few seasons, would continue this mocking.
While NBC was a frequent target of jabs for the show, this was the first episode that heavily involved mocking of FOX, the network on which Married...with Children airs. Most notably is the "Fox Viewing Positions", the drastic measures that the Bundys use to watch the "Pease in a Pod" show and would become a regular gag.
This episode acts as a parody of the FOX Broadcasting Company, which at that time had a tendency to create shows focused on the nuclear family. Married...with Children, FOX's first original show, is an example of that; the network's second original series, the sketch comedy Tracey Ullman Show, birthed another nuclear family comedy: The Simpsons. Both would become two of FOX's flagship shows, but attempts to recreate their magic (including 3 failed spin-offs of MWC) never succeeded.