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.
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)
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