The third world has problems like starvation, war, finding drinkable water and lots of other fundamental problems. The first world has problems like, waiting for more than ten minutes on hold when trying to pay a bill and, being unable to find the correct remote control for the TV. The funniest one I have heard is that someone had to see Harry Potter And The Deathly Hallows in 3D because the 2D showings had sold out.
Reddit has a subgrop called FirstWorldProblems which is full of these although a lot could be argued to be problems for everyone.
Zach who has a channel on youtube called Funnyz did a rap called first world problems.