Revealing mistake: In the sequence when he gets shot by the FBI agents for stealing cable, Jerry Seinfeld is wearing ear buds, quite visible when he collapses by the door. Evidently the stage props even loaded with blanks were too loud for his taste. (00:09:00)
Continuity mistake: When the cable guy tells Jerry it'll cost him 400 bucks, he is holding the plate with the cake in his right hand, but in the following shot the left hand is holding just the fork. (00:19:10)
Continuity mistake: George walks confidently to his ex and calls her by name. Leslie's friend is taking a bite from a little celery stick, but in the following shot her hand is lowered in front of her chest. (00:16:45)
Continuity mistake: In the opening shot of The Baby Shower party, Leslie turns towards her friend and starts talking as a ponytailed woman walks in the background. The same happens in the close-up that follows. (00:12:35)
Continuity mistake: Kramer keeps pestering Jerry with the offer of the illegal cable. On the table behind Jerry, the position of the remote and the cable keep changing between shot in the first part of the scene. (00:06:00)
Continuity mistake: George sits in Elaine's spot and puts his wallet close to a glass of water and a used tissue. When he gets up in the next shot, the glass is further back on the table, past the small plate and closer to Elaine and Jerry. (00:05:40)
Continuity mistake: Elaine sits by Jerry to ask him permission to hold The Baby Shower at his place. Jerry is holding a morsel of food in his hand, gone at the first cut. (00:04:20)
Continuity mistake: Reminiscing about the incident with the performance artist, George says that she was aiming at him with the chocolate syrup "like she was putting out a fire." Notice Jerry has nothing in hand. Next shot and he's clenching a paper tissue. (00:02:40)
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)
