Normals Problem? Claw like Artifact?

I am generating a triangular mesh and trying to display in proper lighting condition.
but i have having two problems while doing so:-

  1. some of my triangles are rendered very bright than the neighbor triangles ( as shown in fig1 attached).

  2. and when i rotate the object, i get a claw like artifact as shown in fig2 attached.

what can be my problem and how to eliminate it.

Can you post how you actually rotate the normals and or object? At the moment you are expecting us to guess all the details!

Here is the simple version of how i computed normal but get the same error.
Initially lets assume we have the triangular mesh. While displaying those triangles… i find out the vector between the two edges and compute the cross product the get the normals at each vertex of the triangle. For triangle ABC, i get the vector AB and AC, the get the cross product between them to get the normal at point A. likewise for B and C.
I am computing this one time only and storing it on display list and displaying by calling display list.

The triangular meshes are for dataset 64 x 64 x 64 so i have taken center[3] as {32,32,32}

I am rotating and translating the object in both x and y direction with zooming facility

here is the code for that:-

glTranslatef(cube_center[0], cube_center[1], cube_center[2]);
glTranslatef(-(cube_center[0] * zoomfactor), -(cube_center[1] * zoomfactor),-(cube_center[2] * zoomfactor));
glScalef(zoomfactor, zoomfactor, zoomfactor);
glTranslatef(deltax, deltay, deltaz);
glTranslatef(cube_center[0], cube_center[1], cube_center[2]);
glRotatef(rX, 1, 0, 0);
glRotatef(rY, 0, 1, 0);
glTranslatef(-cube_center[0], -cube_center[1], -cube_center[2]);

variables meaning:
zoomfactor is initially 1.
rX and rY stores the rotation in x and y direction.
deltax and deltay stores the translation on x and y direction.

I am calling the display list that draws my object after calling this code above.
I have attached the figures for this configuration of mine.

Problem 1: fig3.png -> showing problem where some triangles are very bright or very dark as compared to its neighbouring triangles.

Problem 2: fig4.png -> claws like artifact.

For problem 1, i have tried to make the z value of normal negative if its positive but it didn’t helped.

I dont have any clue about the problem 2 but i see those artifacts when rX goes from 90 to 100,and also for any combination rotation of rX and rY.

i would be very grateful if anyone can help me with this…

thank you