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.
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.
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.
Continuity mistake: When Thing frightens Fester in bed, the candles that Fester is holding instantly disappear from his hand and his bedside table.
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