Continuity mistake: When Elaine joins Jerry and George at The Cafe and tells them she spent ten minutes looking for a grape, keep an eye on the straw in George's drink. From shot to shot, the straw in George's drink keeps changing position, from tilted to upright, then tilted at The Opposite end of the glass, then upright again, then back to tilted.
Continuity mistake: While Kramer is on the phone with the guy who stole Jerry's car, a NY Mets hat is seen upside down on the behind George. When Kramer hands the phone back the hat is now right-side up and facing the camera.
The Sponge - S7-E9
Factual error: During the AIDS walk there is an officer seen several times with a patch "Transit Police, NYC." Not only is the patch completely fictional, it doesn't look anything like the real transit police logo. The Transit Police had already been defunct by the time of this episode.
Continuity mistake: After George and Jerry discuss the fact that George will never have sex again, they stand up to leave the coffee shop and George places a large book under his arm. In the very next shot, he is holding the book in both his hands.
Plot hole: When Elaine meets Glenn's welfare case worker at The Apartment, the case worker does not tell Elaine that Glenn actually has a wife (after clarifying that she isn't The Wife). This is pure plot convenience. When Glenn's wife finds Elaine in The Apartment, he says "You're home early." She lives there, they are not separated, and surely the case worker would be involved with both of them, not just Glenn.
The Calzone - S7-E20
Other mistake: When Kramer is at the restaurant, as a favor for George, he tells the employee that he wants "three calzones." Then the employee just starts cooking the calzones. He never asks what ingredients/filling Kramer wants in those, and Kramer never says.
Other mistake: While Jerry is looking out the window, to his right, there is a Yankees baseball cap on top of his mini basketball hoop, above his computer monitor. Jerry in real life is a Mets fan, and he alluded to being a Mets fan on the show as well (taping a Mets game, wearing or showing Mets paraphernalia). In no universe would a Mets fan have a Yankees cap on display and vice versa. This was before George got the job at the Yankees so that can't explain it. Was it just bad set design and props? (00:14:22 - 00:15:30)
Suggested correction: There's a Yankee hat in many previous episodes. It's never mentioned where it came from, but it could be a gift or signed or hold significant value to Jerry as opposed to him buying himself a Yankees hat to put on display. And that's assuming Jerry in the show is such a Mets fan that he wouldn't like the Yankees as well.
Factual error: Elaine is placed in the same jail cell as the others. No police department anywhere in the U.S. would put a woman in the same cell as men.
The Suicide - S3-E15
Other mistake: While George is talking to Elaine and Jerry in Jerry's apartment, Jerry and George talk about how George's mother and father are both bald. We know from later episodes after his parents are introduced that they both have hair.
The Old Man - S4-E18
Revealing mistake: After The Old Man's dentures are destroyed in the garbage disposal, he shouts that his dentist is "downtown." There is sibilance audible in his production of the T sound (after the stop release). Sibilance is high frequency noise cause by turbulent airflow directed at the front teeth vibrating randomly in a small space; if he had no front teeth, there should be no sibilance. (00:14:35)
Revealing mistake: When Kramer is driving his Tupperware full of blood in Jerry's car, you can tell by how rapidly The Blood is oscillating that it is just red-colored water. As the saying goes, blood is thicker than water, so actual blood wouldn't oscillate that rapidly, especially when it had just been pulled from a freezer. (00:18:20)
Other mistake: The previous episode "The Deal", was supposed to be the season (and possibly series) finale, however it was aired out of order. Therefore in this episode and the next without explanation Jerry and Elaine are not romantically involved anymore, and Kramer pitches cable to Jerry as if he never had it before, mentioning "The naked channel" that was sorta the triggering factor of "The Deal" 's plot.
Suggested correction: As you said, the episodes were aired out of order. That doesn't make it a mistake because if you watch the episode in the order they were produced, there would be no mistake.
Other mistake: When George is taking off his sweater revealing the chocolate-smeared shirt, a woman in the background hilariously stares, looks down at the shirt and then eyerolls. She is behind him, though, and can't possibly have seen the stain. The shirt looks fine from the other angles. (00:16:30)
Continuity mistake: Kramer tries to stop Jerry from running towards the door. "Agent Stone" in the following shot has his badge in the left hand (was in the right earlier) and reaches with the right for his gun under The Jacket. But there's another shot, with cornflakes and other things being blown up by bullets, when Stone is still showing his ID in the right hand. (00:09:00)
Continuity mistake: In the shot when she protests that the husband with the chipper name is only a Kennedy by marriage, Elaine is holding a paper towel, not quite in continuity with what comes before and after. (00:01:35)
Continuity mistake: George grabs the slip of paper from Elaine's hand. When he has his 'heart attack', in the shot when Jerry says "What does that mean?" the paper goes from his left hand to his right hand. (00:02:45)
Continuity mistake: Elaine hands the ice cream bucket to George. George is holding the plastic spoon against the container, in his left hand. In the close-up he reaches for the spoon off-camera with his right hand. (00:20:45)
Continuity mistake: Elaine and Jerry guessed that George is telling them about a heart attack. Jerry says "I know what this is" pointing a finger - but in the next shot not only the hand is pointing a finger; the hand is holding the yellow note. (00:03:05)
Continuity mistake: Jerry is smothering George with the pillow when Elaine walks in. First shot and a black nurse is walking behind her. Cut for one second to Jerry, back Elaine and the same guy is still walking, exactly where the view cut the first time. (00:06:25)
