Agreed. I find writers getting things wrong when there's no artistic or cost implication involved in getting them right, rather distracting, It interferes with my suspension of disbelief. Getting the details of the Nobel procedure wrong have annoyed members of this forum no-end. That's not to mention the way scientific research is presented.
And then there's Sheldon - who says he skipped Kindergarten - writing 'DARk MAttER' and 'PRotOn DEcAy', like a three-year-old, which drives me crackers. Obviously he never caught up. (Strange that, since in Young Sheldon he seems to have got letters right by the age of nine.)
Many people don't understand the niceties of the constitution of other countries or even get the name right. It's quite usual to call The Netherlands 'Holland' for instance, although Holland is the name of a region. Even Mary II in her journal used the term 'Holland' in the 1680s although if anybody should have known the right name, having lived there for twelve years as Princess of Orange taking great interest in its people, she should. Perhaps she was thinking of what her readers would call it. However, one would think highly-paid scriptwriters would expect a highly-educated character with a PhD not to mix up the UK and England. It's like a non-American person calling Mr Trump 'The President of Texas'.
OTOH this little issue has started me thinking about Bernadette's background. On the few occasions she's mentioned her childhood she's not said where it took place. We know she was taking part in a beauty show in the US when she was nineteen, but not how long she'd lived there by then. If she had her early history lessons at school in central Europe, there's no reason she would have been taught, as we were, about The Pilgrim Fathers and other early settlers from the British Isles who were citizens of what was then only unofficially called The United Kingdom, nor the American War of Independence from what was by then officially The United Kingdom. She may know next to no history of the USA at all. In which case, having been immersed in science, she may never have heard of the UK. If so, I forgive her for thinking England has a Prime Minister. England, unlike the other three, doesn't even have its own Parliament, and hasn't had one for over four hundred years. There's no reason Bernadette should know that. She might not even know how American Churchill was.