
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)
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