Here I’m talking about a scene in a show that breaks the rules established in future episodes, or even rules established later in the same episode.
The example I’m thinking of here is on the Deep Space Nine episode " The Search" when The Defiant is boarded by Gem Hedar, a relatively new species, and one of them attacks Odo. We later learn that worship of “the founders” or shape shifters is programed into their genetic code. Since Odo is technically one of the founders as soon as Odo is seen he should not only surrender but call all the ships and tell them to stop firing in order to prevent any possible harm to Odo.
Star Trek’s pretty infamous for having one-shot plot devices that completely break something, or get completely ignored in future episodes, because the episodes were written by a bunch of different people and the continuity police were on break that week.
In Plato’s Stepchildren, they found that some meds that McCoy carried with him in his medikit would make anybody a psychokinetic god.
In the Star Trek reboot, they created the ability to teleport at interstellar distances, negating the need for starships.
In the TNG episode The First Duty, Robert Duncan McNeill played Nicolas Locarno, a classmate of Wesley’s at the academy. When Voyager was created, the producers wanted Locarno to be a recurring character, however they would have had to pay royalties to the writers of The First Duty every time Locarno appeared on Voyager. So, they created a new character, Tom Paris, for McNeill to play, who was basically Nicolas Locarno with a different name.
On Cheers, Frasier claimed his father was dead. On Frasier, guess who moved in with Frasier?
I see this “fact” posted in various places without any cites, credible or otherwise. I doubt very much that it’s true. TV writers are writing “for hire” and as such their work would belong to their employers.
I haven’t seen the 3rd one yet so I don’t know if it’s brought back up, but in the 2nd movie they explain that a secret government project locked it up.
This was explained on an episode of Frasier where some Cheers people appeared. Frasier said that he’d just talked to his father and was mad at him. So he said he was dead.
Almost everything.
Are we talking specifically about moments in early episodes which contradict rules established later in the series, or just random moments of discontinuity? The former is known as Early Installment Weirdness, which happens a lot in long-running shows. The latter is just being sloppy. 
In the pilot for Dead Like Me, the reaper Roxy blithely stands by as a lady is crushed by a ton of bricks, and doesn’t bother gathering her soul until afterwards. It’s later established that the reapers must always “pop the soul” before death, or else the victim will carry the scars of their death for all eternity. And while it does sometimes happen by accident, the callous disregard shown by Roxy in the pilot would be unthinkable, even for her.
This isn’t really a continuity error, but I always thought it was strange how Carmella Soprano, in the series pilot, grabs an AK-47 to confront an intruder (which turns out to be Meadow sneaking back into the house) but never again touches a firearm for the rest of the series.
The shows Emergency! & Adam-12 had some weird discontinuity. Both shows supposedly take place in the same universe, as Reed & Malloy would occasionally guest star on Emergency! However, later in the series, John Gage suddenly becomes an obsessed fan of the TV show Adam-12 .
One from* The Simpsons*: Marvin Monroe, the family therapist, was supposed to be dead (there was a Marvin Monroe Memorial Hospital, and they alluded to his death in a clip episode). Then he reappeared in a later episode several years later. I think the writers brought him back just to fuck with the viewers.
I watched an old Dukes of Hazzard episode not too long ago, having not see it in probably 25 years. I felt like I was going insane it was so different from what I recalled. There was a drunken brawl at the Boar’s Nest, I’d swear Daisy Duke was dressed way sluttier than I expected, and Roscoe P Coltraine was actually serious and smart, not the bumbling idiot I remember.
Then I watched another one, and all of that was gone, replaced by the more clean version from my memories, and Roscoe was once again a moron. Weird.
IIRC that’s also why the character of T’Pol was created for Star Trek: Enterprise; at one point in development she was supposed to be a younger T’Pau, but that would’ve meant paying royalties to the writer of Amok Time every time she appeared onscreen. T’Pau later made a guest appearance as the leader of the Syrranites during the Vulcan Reformation arc.
All of the early events on Friends are completely screwed up. IIRC, Carol was pregnant with Ben for over a year.
There’s Mandy from the first season of The West Wing. She had worked on Bartlet’s campaign, but come season two, she had disappeared - even being written out of flashbacks to the campaign.
Speaking of The West Wing; the first mention of the First Lady on the show was on the context of her dodging rumours she was consulting astrologists, which seems very unlike the Dr* Abigale Bartlet we later got to know.
*I always found it highly irritating when she was referred to as “Mrs”, even before she suspended her medical licence.
Maj. Margaret Houlihan’s father turned up in “MAS*H” after she said he had died. She was very drunk at the time, though.
That must have been a first season episode, before CBS learned of all the impressionable children watching.
No doubt to protect the ship builders union, am I right?
More the first idea where they create rules that were broken previously before they thought of the rule.
Kind of… they wanted to build an armada of warships to use against the impending Klingon war, instead of just transporting a large number of antimatter weapons directly to the surface of the Klingon homeworld…
On the Mary Tyler Moore show, Rhoda had a younger sister named Debbie (we went to her wedding with Rhoda and Mary in one episode), and mentions at least one brother. By the time she got her own show, Rhoda’s only sibling was the depressed and unmarried Brenda.