Render artifacts on hair particles

I downloaded the latest Blender version yesterday and decided to do something quick involving particles. I decided to make a broom. The problem is that every time i make a render, several white artifacts are shown over the particles, i tried on both blender 2.56 and 2.57 and can’t find the way to deal with it. Your help would be very apreciated. Thanks!

The render:

The .blend file: