Today I went out for lunch with my mom and her boyfriend (my parents are divorced since last year) and the cashier asked me what the name of 'my father' was. I was very uncomfortable with someone calling him my father even though it's not her fault at all but I didn't correct her either. Should I have?
Don't bother correcting random strangers for whom it will never matter. If a friend makes the mistake, sure, correct them. However who cares if a random cashier thinks he's your dad. I guarantee you she has probably not thought of you once since.
It's not really a big deal. But I just would have said something like "He's not my father, but his name is ______."
I agree with Lance and I've been in similar situations with my mom and her boyfriend just be try to be cool about it and not freak out just because a stranger made a mistake even though it might bother you, all it takes is simple correction that does not require a life story or retorting at the stranger for a mistake that you have no control over.
I would correct strangers, yes, but I wouldn't flip out over it. It is a bit rude considering that strangers have absolutely no clue at all.