A word that deserves more widespread use is “grievance.” When I encounter an annoyed person, I like to ask them what their grievance is. Grievance implies a sort of entitlement to pity. It’s graver than words like problem or issue, but subtly introduces the notion of whining, making it the perfect soldier of sarcasm.
So, go ahead: with overzealous sincerity, ask distraught people what their grievance is. Watch their faces contort as they try to decipher whether you’re being genuinely sympathetic to the gross injustice that has befallen them or if you’re mercilessly ridiculing them for the petty first-world-ness of their problems.
You and I, we’ll know you’re squarely in the latter camp, but let them believe otherwise.