Revealing mistake: When Carol goes to the dress rehearsal, she is wearing one outfit when she is talking to Mrs. Goodwyn, but then when she goes upstairs to the girl's bedroom and talks to Marcia, she is wearing a totally different outfit.
Audio problem: When Greg and Peter were in the family room helping Marcia write a letter to Davy Jones, Peter suggests telling him that he won a $10 million sweepstake. Then as they walk into the kitchen, you hear Greg saying "A $10 million sweepstake" and Peter says "$20 million?" It is clear that he wasn't really talking, because the sound of his voice is very distant, although they were only in the next room.
Other mistake: When the frog jumps on the pizza (during Greg and Rachel's date), the gooey cheese mess resembles more superimposed tacky glue than actual melted cheese.
Other mistake: When Mike is talking to Mr. Crawford and the operator asks him to deposit another 10 cents, Mr. Crawford said, 'Did I hear an operator ask for 10 cents?' Only Mike would have heard that recording, not Mr. Crawford (he didn't have the pay phone).
Visible crew/equipment: When Mike and Bobby drive up in the station wagon, just as Mike stops the car, on the left side of the screen we can see the edge of the house set. Instead of the usual wood fence in the yard, there appears to be a directors chair (provided to all cast members) in the dark background. (00:05:35)
Dear Libby - S1-E2
Visible crew/equipment: When Carol questions Greg, Jan, and Peter about the argument she heard, Greg tells her it was on TV, and as the three kids sit down the actor's two tapes marks are visible on the floor in front of Peter's feet. (00:10:00)
Career Fever - S4-E9
Plot hole: Peter thinks he has a fatal disease. The parents realise two pages stuck together and he went from page 95 to 98 mistakenly. However, Mike first read about the actual fatal disease info on page 97, and then Carol read about what Peter actually had on page 96 (poison ivy). If Peter read only 95 and 98, there would be no way of Peter to know his disease was fatal since that was printed on page 97.
Lights Out - S2-E20
Revealing mistake: When Peter is on stage at his school for the talent show, Cindy gets into the disappearing lady booth and Peter closes the curtain. He says the magic words, yanks open the curtain and Cindy has disappeared. Look at the top left side of the booth and you can see where the stage curtain is piled up on top of the booth. There is just enough room for Susan Olsen to get out of the booth and then get back in.
Plot hole: When Mike was at the meeting and pulled out the Yogi Bear poster, he said he could find the other cylinder, and was told by one of the other men that they had to catch a plane in 30 minutes. After that, he had to find Jan, and then Jan and Marcia had time to go on about 4 rides and then find the sketches and then start their run across the park. There is no way all of that could have been done in less than 30 minutes.
Confessions, Confessions - S2-E12
Revealing mistake: At the start of dinner, in the wide shots we can see the table and chairs directly on the carpet. When Carol notices the leaky vase and calls for Alice, in the wide shot as Alice approaches the table, now there's plastic sheeting spread across the carpet under the table, as well some visible tubing under the table, presumably for the water stunt. (00:05:45 - 00:08:15)
The Impractical Joker - S2-E13
Continuity mistake: While Myron is on the closet shelf with Carol's shoes, the camel colored shoes repeatedly change between having camel colored heels to dark brown heels. (00:11:35)
The Voice of Christmas - S1-E12
Character mistake: Alice is in Mike/Carol's bedroom trying to find a place to hide a present and can't find room in any closets and chooses under the bed (only to find Bobby there first with the same idea). Why couldn't Alice simply hide the present in her own room?
Audio problem: When Marcia comes downstairs before the dance Alan shows her his new braces, and as they both head toward the door we hear the clear sound of shoes walking on a wood floor, even though they're walking on carpet. (00:23:50)
Visible crew/equipment: While Alice is hemming up Marcia's party dress, when Bobby and Jan walk into the family room the actor's black tape mark is visible on the floor in front of Bobby's feet. Note that it wasn't on the floor at the start of the scene. (00:10:35)
Visible crew/equipment: After Alice trips on the Chinese checkers, when Mike gathers the kids in the family room to update them, the shadow of the moving boom mic is visible at the top right corner of the screen. (00:02:50)
Kitty Karry-All is Missing - S1-E7
Visible crew/equipment: After Bobby walks out of the family room playing his kazoo, when Cindy places Kitty Karry-All on the couch so she can get the bottle, the actor's black tape mark is visible on the floor beside the couch, where Bobby had been standing. (00:02:40)
Alice Doesn't Live Here Anymore - S1-E4
Visible crew/equipment: While "operation Alice" is underway, after Carol tells Alice to stop organizing the canned goods, when Alice places the step stool chair against the wall the black tape mark is visible on the floor where Carol had been standing, and then it's gone as the scene continues. (00:19:00)
Continuity mistake: In the courtroom, as Carol is giving the judge her side of the story, she's looking in the direction of Mr. Duggan the whole time while saying "otherwise he wouldn't have hit me." Then the camera changes angles and instantly Carol is turning from facing the judge back towards Mr. Duggan.
Audio problem: When Carol calls and Mike answers the phone, (after Cindy runs and then the entire salad (bowl) falls to the floor) you can hear Marcia and Jan arguing in the background, but that exact (said) audio is looped if you listen closely - it is an argument from an earlier script that is repeated about 6 times or so during the length of Mike's phone call from Carol.
Continuity mistake: During the filming scene near the end of the episode, Bobby's hat transitions from being in his hands to back on his head, untouched.
Answer: The dangling bracelet was used for dramatic purposes - to keep the audience on edge.