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.
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.
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.
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