Factual error: Peg says she did the taxes and claimed 23 children. First of all, you can't. Max number of dependents is 2-3, and second you have to have birthdates and social security numbers for everyone. You can't just write whatever you want and send it to the IRS. And it's a joint return yet Peg says she didn't sign her name. You have to. So in reality, she would get in trouble too since she actually lied on the tax return.
Plot hole: Al hasn't got enough cash to pay for a pizza and Peggy overmaxes his credit cards. But somehow he manages to buy three flight tickets for Chicago-Las Vegas. Where'd the money come from? Also, when his card is declined, he calls the pizza shop back (they call him "no tip" Bundy), and somehow they know where Peggy maxed out the credit card. (00:05:15)
Revealing mistake: In the scene where Al and his Dad (both played by Ed O'Neill) are sitting on the couch side by side watch the lines of the cushion in the middle. Every time one of them moves you can see where the two separate shots are overlaid. (00:14:15)
Continuity mistake: When Kelly blows up the car near the end, when they show the car before it explodes, you see someone walking on the right side behind the car. Half a second later the car explodes and now someone is walking by the building on the left side of the screen. There wasn't anyone there before.
Other mistake: When Peggy throws the final ball, all the pins fall except for one and the sweep bar comes down. It is then shown wobbling down without the sweep bar in play. This is an illegal drop and would not count under any PBA sanctioned tournament or in any bowling alley in the United States. The bowling alley would credit her with a 299, and Al would have a chance to get a 300.
Plot hole: In this episode Al is about to break Puggy Weaver's record. Peg decides to bowl and scores a perfect score of 300. Problem is Peg is a horrible bowler, as seen in season 2 episode 9. She never bowls with Al or even enjoys bowling, so this episode really makes no sense.
Deliberate mistake: When the family is trying to get money from Al at the start of the episode, he throws it on the ground making the rest of the family to dive on it and you can see Bud get it, then throw the bunch of money in the middle of Kelly, Peg and Bud so they can all get to it instead of taking it all. (00:02:10)