glm::vec3 campos = state->getCamera()->getPosition();
        glm::vec3 objToCam = campos - mPosition;
        objToCam = glm::normalize(objToCam);

        glm::vec3 upAux = glm::cross(glm::vec3(0.f, 0.f, 1.f), objToCam);
        float angleCos = glm::dot(glm::vec3(0.f, 0.f, 1.f), objToCam);

        glm::vec3 rot;
        rot.y = glm::degrees(glm::acos(angleCos));
       
        // First translate so we rotate around the center of the billboard
        glm::mat4 rotMatrix = glm::translate(glm::mat4(), glm::vec3(-16.f, 0.f, 0.f));
        rotMatrix = glm::rotate(rotMatrix, rot.y, upAux);

Or, just use the built in function that does the same thing:

objectMat = glm::LookAt(objectPos, camPos, camUp);

void FreeLookCamera::translateForward(float distance) {
    glm::vec3 forward;

    forward.x = -distance * glm::sin(glm::radians(mRotation.y)) - glm::sin(glm::radians(mRotation.x));
    forward.y = distance * glm::sin(glm::radians(mRotation.x));
    forward.z = distance * glm::cos(glm::radians(mRotation.y)); - glm::sin(glm::radians(mRotation.x)); 

    mPosition += forward;

    mViewMatrix = glm::translate(mViewMatrix, forward);
}

I'm trying to create a billboard that faces the camera, following the Lighthouse3d tutorial and it really isn't working at all.

        glm::vec3 campos = state->getCamera()->getPosition();
        glm::vec3 objToCam = campos - mPosition;
        objToCam = glm::normalize(objToCam);

        glm::vec3 upAux = glm::cross(glm::vec3(0.f, 0.f, 1.f), objToCam);
        float angleCos = glm::dot(glm::vec3(0.f, 0.f, 1.f), objToCam);

        glm::vec3 rot;
        rot.y = glm::degrees(glm::acos(angleCos));
       
        // First translate so we rotate around the center of the billboard
        glm::mat4 rotMatrix = glm::translate(glm::mat4(), glm::vec3(-16.f, 0.f, 0.f));
        rotMatrix = glm::rotate(rotMatrix, rot.y, upAux);

This isn't working as expected.

A) The billboard will follow the camera as long as I am not within a few degrees of 0 on the x axis. As I start to close in to 0 the billboard rotates back to face down the X axis.

b) Rotation of the billboard becomes whacky when I only increase the distance. It starts rotating by large amounts, and faces away from the camera.

That code seems odd... like how you create a vector "rot" and initialize the "y" component, and dont use that vector again, only the y component.

Anyway, it's not immediately apparent what's wrong, but if you just want a rotation matrix that looks back at the camera...

Why not just take your camera rotation matrix and negate the i and k basis vectors (columns 0 and 2), then set the translation equal to your billboard position. That should give you a transform looking back at the camera with the same up vector as the cam. (assumes camera matrix is orthonormal and looks down -k direction)

That seems a lot easier and less error-prone than whatever the above is supposed to do.

Yup, looks like you've messed that up. http://en.wikipedia.org/wiki/Spherical_coordinate_system

glm::vec3 dir = glm::vec3( cos(x) * cos(y), sin(x) * cos(y), sin(y) ); // note i swapped cos/sin on Y from what the wiki states so that y=0 is down and y=pi is straight up

forward = dir * speed;

void FreeLookCamera::rotate(const glm::vec3 &vec) {
    mRotation += vec;

    mViewMatrix = glm::rotate(glm::mat4(1.f), mRotation.z, glm::vec3(0.f, 0.f, 1.f));
    mViewMatrix = glm::rotate(mViewMatrix, mRotation.x, glm::vec3(1.f, 0.f, 0.f));
    mViewMatrix = glm::rotate(mViewMatrix, mRotation.y, glm::vec3(0.f, 1.f, 0.f));
    mViewMatrix = glm::translate(mViewMatrix, mPosition);
}