Other mistake: When Gomez begins to flip through his desk calendar, we see that "today" is Thursday, March 28, 1991. He then turns to the date of the "next quarter". The left hand page shows Thursday, August 8, but the right hand page shows Tuesday, September 9. (00:11:15)
Continuity mistake: While eating with the family, Wednesday's left arm is on the table while she looks to the right. A shot later she is staring down at her food and her arm is lowered. (00:41:52)
Continuity mistake: When Pugsley asks Fester if he likes the blood, his left arm swaps between being under the table to being on the table. (00:57:39)
Continuity mistake: When Thing is using sign language to tell Gomez that Morticia is in danger, there's a blue coffee mug sitting on the table (to Thing's immediate right) that vanishes every time the camera angle reverses. (01:25:00)
Continuity mistake: The chutes that Wednesday and Pugsley use changes positions when Fester chases Wednesday.
Revealing mistake: In the part in the motel where THING is doing morse code on the table to Gomez you can see the cut-out in the table where the guy's hand is sticking through the table.
Continuity mistake: During the play, when Pugsley slices Wednesdays throat, there is blood on the front of her shirt. When she turns to face the audience, the front of her shirt is clean.
Continuity mistake: The Red Indian statue Lurch incinerates at the motel later reappears undamaged.
Revealing mistake: The first time we see Thing running down the hallway at the start of the film, the bluescreen is visible at the top of the screen; where the wrist area begins.
Continuity mistake: When Mrs. Craven introduces Tully to her "son" Gordon, Gordon grabs Tully by the shirt collar with his right hand but in the next shot is using his left hand.
Continuity mistake: Before Gordon lifts Tully against the wall, he grabs Tully by the shirt collar. But in the next shot his hand is around Tully's neck.
Continuity mistake: During the Mamoshka dance, they cut away to Tully and Greta talking, behind them walking around we see guests who are in the ballroom at the same time.
Revealing mistake: During the Mamoshka dance, right when Gomez throws the knife high in the air (the one that lands in Fester's mouth), the camera goes to a wide shot when the knife is in the air, and you can plainly see that the jugglers are Fester and Gomez's stunts.
Deliberate mistake: At the beginning, the carolers are on the porch singing. The camera never pans, so this means that the carolers are facing away from the house (towards Gate) - seems rather odd. The only reasons for this would have been to make the clean camera move through the crowd and up the house.
Continuity mistake: When Thing frightens Fester in bed, the candles that Fester is holding instantly disappear from his hand and his bedside table.
Factual error: At the end of the Mamushka, Fester catches the final knife down his throat. With the length of the blade and the angle at which the knife is in his mouth, the point of the knife should be coming out the back of his head.
Continuity mistake: As they go down the slide, Gomez is in front of Fester. At one point, they change positions for a moment.
Continuity mistake: When Fester comes down to the party and the shot cuts to everyone stopping dancing when Morticia calls for their attention, close to the center of the room is a woman with very frizzy orange hair dancing with a man with lots of facial hair. When the shot cuts back to Fester and Morticia, this couple is right behind Fester near the door to the hall.
Continuity mistake: When Fester tries to access the vault alone for the first time and is grabbed by the chain, he has wearing a vest of things like dynamite. When he exits the chute it's gone.
Answer: He's seen pictures and paintings of young Fester and notices a resemblance. Like you said, no-one had seen him in 25 years, so all that was required was a passing similarity.
Brian Katcher