Actually, I think this expression is more amusing than irritating. It's funny to me when someone says, "Let's not make a big production of this." Calling someone's fixation on a trivial offense a big production suggests that the scenery will give way to a panoramic vista and those irked by the minor error will come dancing in, singing at the top of their lungs, "WHY DID YOU FORGET TO MAKE THE COFFEE????!!!!"
Two more accurately phrased reactions, in my view: "Sorry, but I just made a minor mistake, as everyone does," or "My apologies, but I had a major project I had to complete on a tight deadline."
