Sixteen Years and What Do You Get - S1-E6
Plot hole: Peg maxes out the credit card buying Al anniversary gifts and hiring a caterer. When Al tries to buy a watch for Peg it's declined. Later on Kelly somehow uses the credit card and is able to buy the expensive picture frame at the same store Al tried to buy the watch.
Plot hole: Notice when Steve joins the card game. He looks at his cards and says I'm in. The cards are face up on the table! And for some reason the other players have one card facing out where others can see it.
Poppy's By the Tree (2) - S2-E2
Plot hole: Al and Peg are upstairs with the killer. Both of them are screaming, but downstairs, you can't hear anything. Everyone is sitting around talking. It's not until Al and Peg scream again that everyone runs upstairs. And you can tell the screams were "on cue" also.
Plot hole: Al comes home from work. He purposely doesn't look in the kitchen, so he can act like he's surprised it isn't Peg that brings him a beer. Steve talks and Al acts surprised that he's there. When you walk in the front door you automatically see the kitchen.
Suggested correction: It's quite possible to do this. My house has a similar layout: front door opens into the living room, and the kitchen is at the back of the living room. I can come inside and walk to the couch without paying attention to the kitchen. Plus, Al is cranky after work - he says "Ah, what a day" - and he is focused on getting to the couch and relaxing.
This is the only episode where Al does this... Just because he knows it's Steve and not Peg. Pretty obvious.
Just because something is only shown in one episode, that doesn't mean it has never happened before. And because he said "What a day", it seems that his work day was especially frustrating, busy, etc. It's reasonable that he could focus on getting to the couch, not bothering to look at the kitchen.
The House That Peg Lost - S3-E16
Plot hole: Marcy and Steve live on the left-hand side of Al and Peg yet when they come home and see their house is gone Peg is looking out the window in the front door saying they're looking at the hole now they're looking over here.
Plot hole: Al can't eat because his mouth is numb. So they go ahead and eat. Al can eat after the novocaine wears off and Peg can put leftovers in the fridge. They all act like Al can't eat for days and there won't be any food left.
He Ain't Much, But He's Mine - S4-E5
Plot hole: Marcy gets her hair done like Pegs. Everyone makes fun of her saying she looks ridiculous. All she has to do is wash it! Its obviously held up with hairspray but Marcy acts like there's nothing she can do about it.
You Gotta Know When to Fold 'Em (2) - S4-E17
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)
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.
You Better Shop Around (2) - S5-E22
Plot hole: The supermarket director orders the photographer to take a photo of Al's special shopping cart. Then he turns around a little towards the cart. When the camera flashes, his right shoulder has to be in the whole left side of that picture. (00:07:50)
Plot hole: After Al steps out of the coyote doody he goes to Bud and puts an arm around him. Then they walk together towards the same spot - without looking down. (00:03:35)
So This is How Sinatra Felt - S6-E12
Plot hole: Bud and Kelly hide behind the cash register all day. They talk normally the whole time yet Al doesn't hear a word they say and has no idea they are even there.
Plot hole: Outside the Savoy, Marcy tells Jefferson that at last, they found the Bundys. How did they know that the Bundys were there? The Darcys had not been in touch with them since they were left behind at the airport, and the Bundys only decided much later that they were going to the Savoy.
Plot hole: When Dominique is on TV, she says she got the shoes from Al's store. Then the Amish guy comes out to confirm she broke her leg from the shoe he made. Al says yes. She got the shoes way before Al knew he had no more shoes and before they even hired the Amish guy. How can she break her leg from his shoe if he wasn't hired and making them yet?
Suggested correction: Al was passing the blame.
The correction above is correct.
I Can't Believe It's Butter - S10-E13
Plot hole: Griff doesn't know Peg's mom is Butter. He comes to Al's wanting to meet her. Al gathers the family to talk about what to do. They say Griff can't know its Peg's mom, yet they talk out loud and Griff is standing right there while they are sitting at the kitchen table. It's not until the end of the episode he finds out.