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.
Continuity mistake: Near the beginning, Greg is painting the shutter green, he gets a phone call and goes inside. The paint bucket falls on Bobby because the ladder falls. Greg sticks his head out the window and asks who took his ladder. The shutter now has no paint on it.
To Move or Not to Move - S1-E23
Plot hole: The "unexplained noises" (the strange moaning) heard by Carol and Alice could not be heard so loud and clear from the room they are standing in (like we hear in the show). Greg later admitted the noises were on a tape recorder, which he had to have operated, and since he wasn't in their room, the sound would be lower and from another room in the house. Definitely not like how it appeared to them in the show.
Suggested correction: Greg could have used an extension cord, left the tape recorder in one room and plugged it in to play when he wanted to. That's what I did to my younger sister to make her think a monster lived under her bed; she heard it "breathing" when she was alone in the room.
That partially makes sense. Greg could not control when to start the tape because he has to be in the room to hit play. So the only way this could possibly be correct is if he played the tape before Carol and Alice entered the room, and he recorded it with several minutes of dead air before the noises came on, and left it running the entire time.
Only problem with this theory is, Carol and Alice heard it from at least two different rooms in the house at different times. How could Greg have set up the recorder and played it in advance, before knowing what room they'd be in each time?
Character mistake: While they're dancing and practising in the garage Marsha says "come on Chris", when she should have said Peter.
Is There a Doctor in the House? - S1-E13
Other mistake: At the end of the episode, when they were looking at the chart they created, and Alice was found to add the measles, you see Mike Brady adding the word "Alice." But the kids and Tiger all had columns, but he is adding her as an extra row, which was for the different illnesses, to suggest that Alice was an illness instead of a person having the illness.
You Can't Win 'Em All - S4-E22
Continuity mistake: At the start, when Cindy walks into the kitchen she sets her books down on the counter with the book's binding facing the sink, but in the closeup the book's binding now faces the opposite way, toward the stove. Additionally, the grocery bag which was on the counter right beside Carol, has been moved for the closeup so Carol is in full view, but the bag is now at the very edge of the counter near the stove, which is pretty odd since there's not enough counter there to actually hold the full grocery bag (presumably something else supported the bag off camera). (00:01:30)
Continuity mistake: The home number Mike dials in the men's bathroom to check on the kids, is very different than the home number Carol dials in the ladies restroom. (00:18:30 - 00:18:56)
Visible crew/equipment: A shadow of a boom mic is visible moving across the brick wall just as Alice starts to punch Mike in the stomach.
Audio problem: When Peter is hinting to Carol that he is still growing, the audio changes to being dubbed in from Peter separate from the actual scene after Peter stands up and mentions he wants cowboy boots. Then the audio is back to normal once Peter mentions "Brown" cowboy boots.
Continuity mistake: The kids walk into the kitchen complaining about the noise from Jan's tap dancing. Peter reaches up and grabs his paper sack lunch and then in the next shot he says "talk about noise pollution" while grabbing his lunch for a second time. (00:09:07)
To Move or Not to Move - S1-E23
Visible crew/equipment: When Alice and some of the kids are in the den Bobby gets up to turn off the TV, and the shadow of the moving boom mic is visible on the wall behind Peter. (00:14:05)
Continuity mistake: When Mike walks into the kitchen asking Alice if he can give her a hand, Alice removes two pots from the stovetop leaving the left side clear, but in the shots from the dining room when Alice trips, there are two large pots on the left side of the stovetop, near the edge of the counter. (00:01:20)
The Grass is Always Greener - S1-E24
Visible crew/equipment: When Mike returns home with the grocery bags, as he sets them on the table Alice walks over, and the shadow of the moving boom mic is visible on the swing door behind Mike, at the top left side of the screen. (00:11:05)
Visible crew/equipment: While Mike is fiddling with his golf bag the morning after Tiger disappeared, just as Mike tells Bobby there's nothing to worry about because his siblings are checking the neighborhood, the moving shadow of the boom mic is visible in the top right corner of the screen. (00:02:45)
Continuity mistake: When Bobby attempts to climb the treehouse for the second time, he climbs to the very top and looks up in fright. From his POV we see he has two more wooden bars to climb, despite being at the top a split second ago.
You Can't Win 'Em All - S4-E22
Revealing mistake: When Cindy and her parents get home after the television show, just as Carol and Mike walk down the steps the set's unfinished wood can be seen at the edge of the steps, at the bottom right corner of the screen. (00:22:40)
Continuity mistake: In a first-season episode, Carol is asked by one of her daughters, "How come you never play golf anymore?" indicating she used to play golf. In the later seasons, an episode came out where Carol was first learning to play golf (appearing as if she's never played before).
Dough Re Mi - S3-E16
Plot hole: Greg bought a time spot in the music studio to record a song. He writes a sudden new song for the studio at the last minute and then, next scene, the kids are singing the song in the studio along with background music playing. Where did all the instruments come from and who was playing them? Even if pre-recorded, Greg and the other kids would have just shown up at the studio at their time, and no way they would have been able to get the tracks down in advance to an unknown song like that.