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)

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)
Character mistake: At the end of the episode when all the kids line up to head upstairs, Mike gives instructions to line up according to their size (big to small). If you notice carefully when the kids all line up, Peter stands behind Marcia, yet he is slightly taller than her.
Other mistake: The scene where Alice is giving Tiger a bath was the same one used in "Katchoo Katchoo", albeit with some audio dubbing thrown in, like when Alice complains about the floor getting wet. (00:04:05)
Is There a Doctor in the House? - S1-E13
Plot hole: Lots of factors here: The doctors end up with the opposite kids that they were supposed to have... Why didn't they simply switch in the first place rather than go through all the drama? Also, the male doctor admits Alice let him in and most likely Alice would have told him first door on the right (like she's given directions in other episodes) to locate Peter. And the biggest question of all is, what doctor would make a house call and not look for their patient rather than just ending up with someone else they were not called to see (remember, each parent called their own doctor to see their biological kid).
Suggested correction: The lady doctor goes to see Peter as Mrs. Brady directs her to Peter's room first. Alice likely knows Peter already has a doctor looking after him, as it can be assumed Carol told her, so she sends the male doctor to Jan's room likely explaining to him that Mike's new daughter is also sick and needs to be checked. As to why they didn't solve this doctor problem to begin with; simply they are still a new family and didn't yet think about this as this is the first time the kids are sick.
Visible crew/equipment: When the shelf falls in the store, you can see the rope attached to the top of the shelving unit being pulled from off-screen triggering the collapse of the shelving unit, it was not the girl's weight that made it tip.
Continuity mistake: When the kids are building the card castle to see who would get to choose what they get with the stamps, Jan is putting a card on, in one shot her hair is up in a ponytail then in the other shot her hair is down. This happens back and forth when the shots change.
Other mistake: A final contest is given for control of "green stamps" with all the kids building a "House of Cards." Whomever causes the cards to fall will be the losers. All is going well until Tiger comes in and knocks into Greg and causes him to bump the table and knock over the cards. If you watch closely at the end of the scene, when all the dialog is finished, you can see Mike trying to knock down a few remaining cards. However they keep popping up. Probably due to the fact that the cards were glued together to make it easier for the kids to build upon.
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)

Continuity mistake: When Marcia takes her last turn placing a card at the top of the tall house of cards, in the shots facing her she's stressed about accidentally collapsing the cards so she holds back her charm bracelet with her left hand, but in the first shot facing the three boys Marcia's left arm is down at her side and the charm bracelet is dangling at her wrist, right beside the cards. (00:21:00)
Other mistake: Carol grabs a pot holder with her right hand and removes a small cake from the oven. The cake pan is obviously not hot. It starts to tip and Carol steadies it by placing her bare left hand on the underside of the pan.

Visible crew/equipment: In the episode where Alice sprains her ankle, Sam comes over and gives Alice some flowers. He leaves, and Mike walks in and the camera zooms into Alice and you can see the boom mike shadow on Mike's face. (00:14:00)
Is There a Doctor in the House? - S1-E13
Audio problem: When Mike walks into the kitchen and sees the chart with the list of kids on it and what ailments they've had, he comments on one of the ailments, saying "None of the kids have had distemper." However, if you watch his mouth, he appears to have originally said "rabies."
Continuity mistake: The shadow (supposedly of the window frame) on the headboard of Jan's bed changes from one shot to the next. (00:24:35)
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)