Continuity mistake: In the scene where Margaret Thatcher is teaching her daughter Carol to drive, you see Margaret's window partially open but just as they near-hit the cyclist, her window is down just enough for her to stick her hand out but in the next shot its back to being partially open.
Factual error: In the medicine cabinet, when Margaret is emptying it, a box of Rite-Aid Bandages is visible. Rite-Aid is an American chain of drug stores, not in the UK. And the Brits call the product plasters.
Other mistake: In the scene where Margaret is wearing a bright-blue dress and a woman is sewing a button onto it while about six men stand around and wait, the woman finishes sewing the button on, but keeps on going, even though it's fixed. The whole thing takes ten times longer than it should.