Why haven't Earth and Venus got any tiny moons? Or have they? Why haven't some meteoroids gotten caught in Earth's or Venus' orbit?

AFAIK most meteors are tiny fragments from comets. Shouldn't some comet tail sometime have passed Earth orbit at velocities suitable for our planet to capture such fragements? And 100 000s of asteroids have been detected. Why haven't the inner planets gotten asteroid like moons like the outer planets have? The asteroid belt isn't too far away.

Earth's large Luna might clean them away, but that won't explain Venus' lack of tiny moons.
The strength of the Earth's gravitational field compared to the Moon and the Sun is not enough to capture and hold satellites - there are too many disruptive forces that would rip them away over time.

However there are some objects at the Lagrangian points - the points where the gravitational fields of the Earth and other objects are equal and so it is possible to have a (likely-meta) stable orbit. 

This gives some details about what might be found at the various Lagrangian points: http://en.wikipedia.org/wiki/List_of_objects_at_Lagrangian_points