I will give people a pass on "expresso" if they don't drink it or otherwise interact with it on a regular basis. I confess, for the longest time I thought that was actually the name of the coffee-and if you think that's really the name, then you aren't pronouncing it wrong, as such. Your mistake is in what you think the stuff is called.
But if they drink it on a regular basis (or pick it up or serve it to other people) and they still say it that way, that's really irritating.
And "axe" for "ask"? Just wrong.