Character mistake: When Bud is showing Al his school project of a fan page turner, he has it on the left side and blowing the pages left to right. That would be blowing the pages the wrong direction to flip pages. It should be on the right side changing pages right to left.
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.
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.
Continuity mistake: Al and Bud are being hunted because they are the final male Bundys. However, earlier, in Baby Makes Money (Season 4?) Al and Peg went to the funeral Of Al's uncle, Stymie. There were other male Bundys. The heirs had to produce a male heir and name him after Uncle Stymie to get all the inheritance. The 3 England Show episodes all have the premise that Al and Bud are the only male Bundys left.
Revealing mistake: When Al slams Kelly's date's head on the banister it moves back and forth indicating it's made of rubber.
Other mistake: When the fat woman gives them the straws, there is no reason why one would already be cut short. They didn't cut the straw. How did they get a short straw?
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.
Dead Men Don't Do Aerobics - S4-E2
Other mistake: Jim Jupiter stays with Peg for a week. 6 days later he's shown heavier than he was before. You don't gain that much weight in 6 days.
Continuity mistake: When the chain is cut with Marcy by Al to release him from the pole, later in the newscast in the background they are showing the cut chain. When on the news, it shows the chain was cut about a foot from the goal post. However when you watch the guy cut the chain for real, he cuts it flush with the pole.
Just Married ... With Children - S2-E20
Other mistake: Al gets sat on by 3 heavy women. The scale says 927 pounds. 4 more women sit down and the scale says 1071. So 4 more heavy women only added 144 pounds? Impossible.
Just Married ... With Children - S2-E20
Other mistake: Al and Peg win a new Mustang in this episode. It's never seen again.
The Hood, the Bud and the Kelly (2) - S10-E15
Revealing mistake: Whenever Al or Jefferson falls off the roof you can plainly see it's a dummy wearing their outfits.
Chicago Shoe Exchange - S11-E24
Factual error: When Kelly and Jefferson are driving Bud to the chiropractor and puts him on the roof of the car, as they are driving palm trees are lining the road. There are no palm trees in northern Illinois anywhere, let alone lining roads.
Factual error: Al gets hired as a bartender despite having no liquor license and not having taken the course required to become a bartender.
Suggested correction: Depending on the bar all you need is a diploma or GED and be old enough per the state's laws.
Flight of the Bumblebee - S10-E7
Continuity mistake: Jefferson mentions having Thanksgiving dinner at Marcy's father's house. Yet, in the pilot, it's mentioned he's dead, as well as her two stepfathers.
Revealing mistake: When Kelly goes for her commercial, you can see that there is a stocking head cover to make her appear bald.
Visible crew/equipment: When Buck is sitting on the couch before Al and Bud come back, the shadow of the camera boom can be seen moving on the stairs.
Continuity mistake: In this episode Al is building a dog house for Lucky. In Season 9 episode User Friendly, we are shown that there already is a dog house, which has electricity and a light.
Girls Just Want to Have Fun (1) - S2-E5
Continuity mistake: When we first see Peg and her friends at the kitchen table the fridge door is closed. Steve comes in with flowers and the door is open. He goes into the kitchen and it's closed.
Have You Driven a Ford Lately - S1-E5
Continuity mistake: Marcy gets two cans of soda for her and Peg to go with their salad. Camera changes shots and it's now two glasses of soda.