Q: Optimize OpenGL Fragment Shader I have a vertex/fragment shader that draws a rectangle performing many calculations based on a texture. (It blends pixels, modifies them, etc). The thing is that each rectangle and the pixels it contains will not change. I only move the entire rectangle(s) around and zoom them.
Is there any way to optimize the fragment shader since the rectangles do not really need to be recomputed?

A: So, if I understood you correctly you compute those rectangles once and then want to reuse them? This kind of task is solved by rendering to a texture and then use the generated textures further on.
Render to texture is easiest done through Framebuffer Objects.
EDIT: A simple example for using FBO to render to texture
// test_fbo_teapot.cpp

#include <GL/glew.h> // Uses GLEW for extension loading
#include <GL/glut.h> // Uses GLUT as framework
                     // Check those are on your system for compilation
                     // and if not please install them.

#include <cmath>
#include <iostream>

using namespace std;

namespace render
{
    int width, height;
    float aspect;

    void init();
    void reshape(int width, int height);
    void display();

    int const fbo_width = 512;
    int const fbo_height = 512;

    GLuint fb, color, depth;
};

void idle();

int main(int argc, char *argv[])
{
    glutInit(&argc, argv);
    glutInitDisplayMode( GLUT_RGBA | GLUT_DOUBLE | GLUT_DEPTH );

    glutCreateWindow("FBO test");
    glutDisplayFunc(render::display);
    glutReshapeFunc(render::reshape);
    glutIdleFunc(idle);

    glewInit();

    render::init();
    glutMainLoop();

    return 0;
}

void idle()
{
    glutPostRedisplay();
}

void CHECK_FRAMEBUFFER_STATUS()
{                                                         
    GLenum status;
    status = glCheckFramebufferStatus(GL_DRAW_FRAMEBUFFER); 
    switch(status) {
    case GL_FRAMEBUFFER_COMPLETE:
        break;

    case GL_FRAMEBUFFER_UNSUPPORTED:
    /* choose different formats */
        break;

    default:
        /* programming error; will fail on all hardware */
        throw "Framebuffer Error";
    }
}

namespace render
{
    float const light_dir[]={1,1,1,0};
    float const light_color[]={1,0.95,0.9,1};

    void init()
    {
        glGenFramebuffers(1, &fb);
        glGenTextures(1, &color);
        glGenRenderbuffers(1, &depth);

        glBindFramebuffer(GL_DRAW_FRAMEBUFFER, fb);

        glBindTexture(GL_TEXTURE_2D, color);
        glTexImage2D(   GL_TEXTURE_2D, 
                0, 
                GL_RGBA, 
                fbo_width, fbo_height,
                0, 
                GL_RGBA, 
                GL_UNSIGNED_BYTE, 
                NULL);

        glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
        glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
        glFramebufferTexture2D(GL_DRAW_FRAMEBUFFER, GL_COLOR_ATTACHMENT0, GL_TEXTURE_2D, color, 0);

        glBindRenderbuffer(GL_RENDERBUFFER, depth);
        glRenderbufferStorage(GL_RENDERBUFFER, GL_DEPTH_COMPONENT24, fbo_width, fbo_height);
        glFramebufferRenderbuffer(GL_DRAW_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_RENDERBUFFER, depth);

        CHECK_FRAMEBUFFER_STATUS();
    }

    void reshape(int width, int height)
    {
        render::width=width;
        render::height=height;
        aspect=float(width)/float(height);
        glutPostRedisplay();
    }

    void prepare()
    {
        static float a=0, b=0, c=0;

        glBindTexture(GL_TEXTURE_2D, 0);
        glEnable(GL_TEXTURE_2D);
        glBindFramebuffer(GL_DRAW_FRAMEBUFFER, fb);

        glViewport(0,0,fbo_width, fbo_height);

        glClearColor(1,1,1,0);
        glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );

        glMatrixMode(GL_PROJECTION);
        glLoadIdentity();
        gluPerspective(45, 1, 1, 10);

        glMatrixMode(GL_MODELVIEW);
        glLoadIdentity();

        glEnable(GL_LIGHT0);
        glEnable(GL_LIGHTING);

        glEnable(GL_DEPTH_TEST);
        glDisable(GL_CULL_FACE);

        glLightfv(GL_LIGHT0, GL_POSITION, light_dir);
        glLightfv(GL_LIGHT0, GL_DIFFUSE, light_color);

        glTranslatef(0,0,-5);

        glRotatef(a, 1, 0, 0);
        glRotatef(b, 0, 1, 0);
        glRotatef(c, 0, 0, 1);

        glutSolidTeapot(0.75);

        a=fmod(a+0.1, 360.);
        b=fmod(b+0.5, 360.);
        c=fmod(c+0.25, 360.);
    }

    void intermediary()
    {
    }

    void final()
    {
        static float a=0, b=0, c=0;

        glBindFramebuffer(GL_DRAW_FRAMEBUFFER, 0);

        glViewport(0,0, width, height);

        glClearColor(1,1,1,1);
        glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );

        glMatrixMode(GL_PROJECTION);
        glLoadIdentity();
        gluPerspective(45, aspect, 1, 10);

        glMatrixMode(GL_MODELVIEW);
        glLoadIdentity();
        glTranslatef(0,0,-5);

        glRotatef(b, 0, 1, 0);

        b=fmod(b+0.5, 360.);

        glEnable(GL_TEXTURE_2D);
        glBindTexture(GL_TEXTURE_2D, color);

        glEnable(GL_DEPTH_TEST);
        glEnable(GL_CULL_FACE);

        glEnable(GL_BLEND);
        glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

        glDisable(GL_LIGHTING);

        float cube[][5]=
        {
            {-1, -1, -1,  0,  0},
            { 1, -1, -1,  1,  0},
            { 1,  1, -1,  1,  1},
            {-1,  1, -1,  0,  1},

            {-1, -1,  1, -1,  0},
            { 1, -1,  1,  0,  0},
            { 1,  1,  1,  0,  1},
            {-1,  1,  1, -1,  1},
        };
        unsigned int faces[]=
        {
            0, 1, 2, 3,
            1, 5, 6, 2,
            5, 4, 7, 6,
            4, 0, 3, 7,
            3, 2, 6, 7,
            4, 5, 1, 0
        };

        glEnableClientState(GL_VERTEX_ARRAY);
        glEnableClientState(GL_TEXTURE_COORD_ARRAY);

        glVertexPointer(3, GL_FLOAT, 5*sizeof(float), &cube[0][0]);
        glTexCoordPointer(2, GL_FLOAT, 5*sizeof(float), &cube[0][3]);

        glCullFace(GL_BACK);
        glDrawElements(GL_QUADS, 24, GL_UNSIGNED_INT, faces);

        glCullFace(GL_FRONT);
        glDrawElements(GL_QUADS, 24, GL_UNSIGNED_INT, faces);

        glDisableClientState(GL_VERTEX_ARRAY);
        glDisableClientState(GL_TEXTURE_COORD_ARRAY);

    }

    void display()
    {
        prepare();
        intermediary();
        final();

        glutSwapBuffers();
    }
};

