The Jeff Foxworthy Show has an in-universe example. Jeff and his college professor father-in-law Elliot are dressed as a gladiator and the devil respectively trying to milk a nervous cow, Don't Asklong story. Elliot comes up with the idea of relaxing the cow by sing the Indianan University song. When Jeff explains the incident to his wife she says "I remember hearing my father singing that through my bedroom wall as a kid." She and Jeff look over at her parents and realize why her father was singing it.
Arrested Development - in one episode, Barry Zuckercorn makes an offhand comment like "Why do I keep getting all these bruises?" Easily dismissable, right? Not so much when you recall Barry's habit of picking up prostitutes (of both genders, apparently) and have just watched Philadelphia.
The fourth season of Nash Bridges had a Running Gag where a "phantom disco" (complete with strobe lights) in the unit's headquarters (a former nightclub) would come on occasionally without warning or explanation. The problem is finally fixed in season five which is a good thing because season six sees the introduction of Antoine, an epileptic. Had the problem not been fixed, the poor guy would have had a seizure every time the strobes came on.
An episode of Canadian children's show Ready Or Not has preteen heroine Amanda exploring her Jewish roots. At one point, she's horrified to see that the synogogue has been vandalized, a swastika has been spraypainted on the side and she hears somebody yelling anti-Semetic slurs. The kids she's with don't seem to have much of a reaction at all and her classmate calmly tells another kid to tell the Rabbi. When you think about it you realize that this is probably because it happens so often that it's an accepted part of Jewish life.
Fringe establishes in the season 3 episode "Amber 31422" that people trapped in amber are conscious the whole time. Then in season 5, Walter, Astrid, Peter, and Olivia are all revived after being encased in amber for 20 years. Walter has brain damage and doesn't remember it, and what about the others? It helps explain the difficulties between the reunited Peter and Olivia, who were having a rough patch before being separated. They have been thinking about the occupation, the resistance plan, and the safety of their missing daughter for 20 years and couldn't do a single thing about it. It's never mentioned in the series, but it's there in the background making season 5 even grimmer than before.
The Big Bang Theory Sheldon, his Eidetic memory is played for laughs, but the horror comes when you realize he remembers EVERYTHING with excruciating detail, including every last hurt, every last insult, every last time he was picked on as a child, which happened a great deal, and he can remember it all as if it just happened.
Seinfeld: In The Pony Remark when Jerry gets defensive about inadvertently insulting Manya, he starts asking why someone would emigrate to America, a ponyless country, from a "pony-packed country". Manya was in her seventies, Jewish, and from Poland. It's a fair bet that she either left to flee the Nazis, or left after the Second World War to escape the bad memories.
Another from Seinfeld: Wilhelm seems just as zany as everyone else, until you get to The Bottle Deposit. He seems to have serious mental deficits as he is unable to remember things that he had done moments earlier; his wife notes that he had "forgotten to take his medication again". George's project led to institutionalization, it can only be assumed that Wilhelm completed it and had forgotten about it. In The Fatigues, Wilhelm gleefully announces George as his protege during George's Risk Management speech about Ovaltine...all signs point to Wilhelm suffering from Alzheimer's or dementia, making his zany antics seem all the more horrifying.
Are You Afraid of the Dark?? has the "Tale of the Pinball Wizard" episode. When Ross, the protagonist, finds himself trapped in a twisted version of his local mall, the first strange event that occurs is that thousands of quarters fall from the ceiling. When it's later revealed that he's trapped inside a pinball machine, this takes on new meaning: every one of those quarters is a credit in the machine, and thus a round of the game he has to play before escaping, if he ever can escape.