More of a changed premise than a Goof: in the pilot Open All Hours (1973) Nurse Gladys - played by Sheila Brennan - has a pronounced Irish accent which she doesn't once Lynda Baron takes over the part for the series.
Arkwright is supposed to be engaged (on and off) to Nurse Gladys Emmanuel, yet in several episodes, he is wearing a wedding ring. It's particularly noticeable when he's counting money from the till.