Weird shadow artifacts

I used the default hemisphere lamp. How do I get rid of these little devils?

Hemi lights don’t generate shadows, instead they generate a constant light falloff. Maybe you have some other light giving out those artifacts. Have you checked?

The scene consists of a camera, the hemisphere light and the model which is a single object. Help?

It looks to me like more of a normals or smoothing problem. Perhaps try converting those tris into quads, then recalculate normals (Cntrl N).

Not a problem with normals. How would I convert polys to quads?

Go into Edit Mode, select the faces and use the hotkeys ALT+J. But the best thing is to do it by hand, you can easily get rid of a few triangles there.