Episode Four - S1-E4
Other mistake: Jake is sitting at the kitchen counter top and is watching TV whilst doing his homework. You can see his red pencil case labelled 'Jake Rowlings'. Many times throughout the series the parents have been recognised as Mr and Mrs Brockman - not Rowlings. The children also have been referred to as Karen Ben and Jake Brockman. (00:13:40)
Suggested correction: Throughout the series, the Brockmans (specifically Pete and Sue) seem very ashamed of their family. In the first episode they tell Jake to give people Grandad's address. It doesn't seem out of character at all for them to tell Jake to give people a false surname. Also, Harry Potter came out at the same time so Rowling would be a very easy surname to choose. This isn't out of character for the parents at all if you look at the rest of the series.
The family's surname is not mentioned (other than on the pencil case) at any point in the first series. Likewise, the grandad is not named in the first series either. Sue even says she doesn't know anyone called Frank Morrison during Series 1 when Pete mentions a colleague of that name. This creates continuity errors when the family are given the name Brockman and Sue's father is established to be called Frank Morrison from Series 2 onwards.
Episode #3.6 - S3-E7
Other mistake: When Pete goes to turn off the car alarm, you get a look at the key he uses, this key is for a Vauxhall Corsa, and this isn't the car that's going off, it's not even by the same manufacturer. (00:12:15)