why are the graphics so bad?

[yikes]

The graphics are especially bad for the specular light which I've marked with a red square. What can anyone do about it? Everything else looks good though...

[Alfonse Reinheart]

What is this a picture of? What is it trying to be, and what is the glowing thing that you have in a red box?

Without knowing what this is supposed to be a picture of, it's rather hard to know what the problem is or how you might correct it.

[yikes]

I have a point light source where the cube is. The glowing thing in the box is the specular light component of the point light source. I don't think opengl rendered it well...and you can see it is really bad if you enlarge the picture.

[ZbuffeR]

Do you use vertex lighting ? Then this is expected.
You should instead do fragment shading using GLSL.

[mhagain]

Yeah, lighting per-vertex was the first thing I thought of too.

Basically: if graphics are bad, it's because you coded them to be bad. In the case of classic fixed pipeline OpenGL lighting (which it seems you are using), it has always been (and has always admitted to be) a crude approximation that will break under many circumstances. Without an understanding of this, of how the algorithms work, and of where the break-points are, you're going to come across such circumstances more and more.