Revealing mistake: Kelly is making popcorn on the stove. It starts popping even though the heat isn't even on.
Deliberate mistake: Why would Al have his Polk High football uniform in England?
Suggested correction: Al cherishes his memories as a high school football player. It's quite possible that he takes the uniform with him on some trips, especially when going to another country. I've known people who do this with items that are important to them; i.e. a jewellery box or a favourite picture of family. They feel better keeping the item with them, in case something happens at home while they are away.
Peggy Loves Al, Yeah Yeah, Yeah - S2-E17
Other mistake: When Bud goes upstairs with his fake bag of "Valentines" (actually a bag filled with bottles), Kelly begins to look through some from her bag. Behind her, you can see David Faustino (Bud) purposely moving slowly up the stairs because Christina Applegate (Kelly) is about to find the envelope that is addressed to Bud.
You Gotta Know When to Fold 'Em (2) - S4-E17
Factual error: Bud and Kelly wouldn't be allowed to go in a casino in Vegas because they are both under 21.
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.
Visible crew/equipment: When Marcy announces they only have time to grab their most precious personal possessions Kelly notes her own, and in the next shot the boom mic makes a happy appearance at the top of the screen. (00:07:45)
Revealing mistake: Marcy dries her dress in Peg's dryer. She comes downstairs with it on looking like it shrank. You can plainly see Marcy put on her belt and pulled up her dress to make it look shorter.
Factual error: Griff's shown being strapped into the electric chair. Problem is Illinois had stopped using the electric chair and switched over to lethal injection in 1983.
Other mistake: Al, Peg, and the kids go to the beach. Steve and Marcy are sitting not too far away from them, yet they never interact with each other. They had to see each other they just act like they don't notice each other.
Factual error: The sheriff does not come to your house and take your credit cards just because they are maxed out. The only time they would do that is if you stole someone else's card and were using it.
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.
Continuity mistake: After Bud's Hail Baby, the spoon that had been to the right of Peggy's glass, changes position.
Continuity mistake: When Al and Peg are on the couch, the ice bag changes position.
Visible crew/equipment: When Bud and Kelly are sitting on couch, after Al goes upstairs, you can see the shadow of crew/equipment go across Bud's shirt from right to left.
Build a Better Mousetrap - S2-E15
Revealing mistake: Al smashes his finger while holding a piece of cheese next to the hole in the wall. But you can see the hammer wasn't near his finger at all. It hits the wall.
Revealing mistake: Obvious dummies when Al tosses Peg off him on one of their separate beds and when Al falls through the bedroom floor to the den.
Other mistake: When Sonya takes off Bud's bandages on his arms you can see they aren't injured.
Kelly Doesn't Live Here Anymore - S7-E8
Revealing mistake: You can plainly tell that Kelly is wearing a beehive wig at the diner when Peg comes and talks to her.
You Better Shop Around (2) - S5-E22
Revealing mistake: Watch Jefferson and Marcy's feet at the end. They start to trip before the turkey even hits their feet.
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.