Episode One - S1-E1
Continuity mistake: When Pete is trying to get the drill back from Ben (before Pete says "I'll give you a fiver if you give me the drill"), the position of Ben's hands on the drill change between shots.
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 #4.6 - S4-E6
Continuity mistake: When Pete asks the man if they can have it in writing as they are having a family dinner, the kitchen door is closed, then the shot goes back to the man they are talking to at the front door, in the next shot which returns to Sue and Pete in the space of less than 2 seconds the kitchen door has been opened. (00:01:10)
Episode Four - S2-E4
Continuity mistake: When Karen is drawing in the airport asking about what other religions are responsible for damaging aircraft, the pencil she has changes colour constantly. Sometimes she doesn't have a pencil at all.
Episode two - S1-E2
Continuity mistake: When Sue gives the house phone to Jake while she's talking on her mobile, Jake takes it with his right hand but he takes it again in his left hand in the very next shot.
Episode #3.4 - S3-E5
Continuity mistake: When Lance says "This is a bloody joke", he throws his racket on the floor. The racket then reappears and disappears over the course of his following lines.
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)
Episode #4.2 - S4-E2
Continuity mistake: When Ben is serving the puree/meal he created, firstly he removes the lid from the serving dish with his left hand. It then reappears in his right hand. Also the ladle Ben is holding to serve his concoction switches hands for the next three shots.
Episode #5.3 - S5-E3
Continuity mistake: At the end of the episode when Peter has seen Stacey undressed, Sue comes up the stairs and Ben is standing on the landing behind her. The position of Ben's arms is different in the close-up of Sue than it is in the wider shot from from behind Stacey.
