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.
Suggested correction: This is not a plot hole, but a plot point. Yes, Peg is a horrible bowler, but it's typical Al Bundy luck that his wife would be able to put together a perfect game no matter how unlikely.
So this one and only episode she scores a perfect game? Highly unlikely. Oh and she's wearing a long evening dress too which would make it difficult to bowl. So this episode makes no sense.
It makes perfect sense. In the world of the show, the universe is out to screw Al over. The worst that can possibly happen to him will happen no matter how unlikely.
It is a comedy, so having all those "strikes" against her, she still managed to bowl a perfect game - leaving Al hopeless and hapless.