Continuity mistake: While George is telling the whale story in the coffee shop, the ketchup bottle on the table disappears and reappears between shots. (00:19:00)
Continuity mistake: When Kramer is talking with Elaine and her coworker in the publishing office, his cigar appears and disappears between shots, as well as switches from his hand to his mouth in others, and from lit to not lit in others. (00:01:05)
Continuity mistake: When George is with his girlfriend at the coffee shop, the ketchup bottle on the table switches between being knocked over and stood up in different shots, despite nobody ever touching it. (00:03:10)
Continuity mistake: When Elaine is on the phone in Jerry's apartment, she holds the phone with one hand and lets the phone cord hang straight in one shot, and in the next shot she has the cord bunched up in her hand. (00:00:50)
Continuity mistake: After Kramer walks into Jerry's apartment, he shuts the door. However, in another shot a couple seconds later, the door is inexplicably wide open. (00:01:45)
Continuity mistake: During a conversation with Kramer, Jerry is holding a drink in his left hand. Although he is never seen setting it down, the drink disappears in the next shot and he has his arms crossed. (00:02:10)
Audio problem: The end of the word "bluey" that George is saying is cut off suddenly at a change to the shot of Jerry. (00:20:20)
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: At the beginning of the episode Jerry tells Elaine that he vaguely remembers "doing something"; Julia Louis-Dreyfus puts the remote down and brings her hand up twice in two separate shots. (00:01:30)
Continuity mistake: Elaine walks up to George in bed, and she asks him if anyone's got his apartment yet. For the brief part of dialogue about the zen lifestyle thing, the top sheet is rolled up in a noticeably different way from the rest of the scene. (00:07:00)
Continuity mistake: On his deathbed George triumphantly utters "There's nothing wrong with me!"; the doctor cools his enthusiasm down though, saying that he wouldn't go that far. His hands are crossed in front of his body - at the cut though he's suddenly already browsing through George's medical file. (00:08:10)
