Just Married ... With Children - S2-E20
Revealing mistake: When Al spins Peg on the wheel to win the bowling ball, in the long shots, you can plainly see its not really Peg on the wheel. It's a dummy.
Master the Possibilities - S2-E16
Factual error: A credit card company doesn't send random cards to just anyone. One comes for Buck. First of all you need a social security number, proof of income etc. And looking at what Al and Peg bought, it's an unlimited card.
Suggested correction: Decades ago (including the 1980s when this show aired), credit cards were sometimes sent to almost anyone - or "anything", such as a family's dog. People used to joke about actually getting a credit card for their cats, dogs, infant children, etc. Credit card representatives also went on campuses to lure "unemployed" students into getting credit cards by offering a free gift. They hoped college students would buy what they wanted or needed and parents would bail them out (pay the bills).
Suggested correction: It should be pointed out that credit card companies, especially in the past, do send out random cards (and offers). They buy customer information from stores from various sources, like warranty cards. People who have received credit cards for their pets (which has happened) have often filled out warranty cards with their pets' name but the rest of the information is the person's.
And some of the "less than honest" recipients of unsolicited credit cards were able to use the cards practically immediately, so went on shopping sprees and charged thousands of dollars for whatever they wanted with no intention of paying or being identified. And not all college students had parents that would bail them out, resulting in huge losses. It took a while, but the credit card companies learned from their mistakes and made drastic changes to avoid getting ripped-off in the future.
Just Married ... With Children - S2-E20
Factual error: In the game show near the end, when Marcy and Steve come out as Al and Peggy. When the real Al and Peggy win the car, because they used Marcy and Steve's names, the car would have never gone to the real Al and Peggy. In reality, it would have gone to Steve and Marcy because it was won under their names. Al and Peggy would not have been able to keep the car. In fact Al and Peggy would not have been allowed to be on the show at all using someone else's name.