Character mistake: Lori said "Lori, let me. It's no big deal." to Jennifer instead of saying "Jennifer, let me. It's not big deal." (00:13:20)
Bad Hair Day - S1-E1
Visible crew/equipment: When Katie is handed the iPad with Alexa on face time, when the iPad is facing the classroom, in the camera reflection on the iPad, all of the stage lights are visible. (00:21:40)
Picture Day - S1-E6
Continuity mistake: I'm not sure what type of mistake this counts as, but in here it is. In the episode "Speaking of Cancer" in season four, Jennifer reveals that she has been lying to Jack and Katie about them all having a shellfish allergy for years because it costs too much for them all to eat it, but in the season one episode "Picture Day" Dave puts down a plate and Jennifer says "Ooh are those crab-cakes?" and takes one to eat. Jack was sitting next to her, so he should have heard this and tried to stop her.
Bad Hair Day - S1-E1
Continuity mistake: The cookies that Jack is counting goes from a pyramid of 3, to 4 cookies in a single stack, and then there are 3 cookies are in a triangle formation. (00:13:00)
Ungroundable - S1-E4
Visible crew/equipment: After Gwenny leaves Alexa struggles to put the bear into her locker and you can see a reflection of the end of the set.
Winter Luau - S1-E9
Other mistake: When Lucas is about to take Alexa from her friends, you can hear them re-using an audio clip from a previous episode, "But if I tell them the same thing is gonna happen to me" which would only apply if this was before Alexa tells everyone that she is the one with cancer.
Continuity mistake: Nurse is handed a stack of cookies which mysteriously disappear when it pans back.
Winter Luau - S1-E9
Other mistake: While Lucas sings the breakfast song, Lori starts filming after the part where he says "Ate my eggs, ate them good" while they are at school. Dylan and Cameron later tease him about how he eats his eggs, but that part wasn't recorded.
