First off, stop acting like you're smarter than you are.

The gravitational force exerted on the earth by people is so miniscule that it wouldn't affect ANYTHING, let alone the collective force of a billion people's impact.

There are, however, flaws in the plan, and they are as follows:

1) The pushoff of each person jumping would exactly counteract the force of their landing. Ever heard of equal and opposite force? When you push up, you have a certain initial velocity. Your acceleration is constant throughout your entire jump (-9.81m/s/s). Thus, when you hit the ground, you have the exact same force as when you pushed off because your velocity has the same magnitude but it is in the opposite direction.

2) The different times for everyone to jump, based on their time zones, are the exact same time... mjord was mostly right in saying that everyone jumping at the same time would have a cancellation effect. It would be slightly different based upon variables such as elevation (the pull of gravity is different at different heights), weight, and strength of the people jumping. Still, this wouldn't likely make much difference in the actual outcome.

What is it they say about silence being golden?