Given the frequent lack of a reference image or ground truth when performance testing Bayer pattern color filter array (CFA) demosaicing algorithms, two new no-reference quality assessment algorithms are proposed. These new quality assessment algorithms give a relative comparison of two demosaicing algorithms by measuring the presence of two common artifacts in their output images. For this purpose, various demosaicing algorithms are reviewed, especially adaptive color plane, gradient based methods, and median filtering, with particular attention paid to the false color and edge blurring artifacts common to all demosaicing algorithms. Classic quality assessment methods which require a reference image, such as MSE, PSNR, and ΔE, are reviewed, their typical usage characterized, and their associated pitfalls identified. With this information in mind, the motivations for no-reference quality assessment are discussed. The new quality assessment algorithms are then designed for a relative comparison of two images demosaiced from the same CFA data by measuring the sharpness of the edges and determining the presence of false colors. Demosaicing algorithms described earlier are evaluated and ranked using these new algorithms. A large quantity of real images is given for review. These images are also used to justify those rankings suggested by the new quality assessment algorithms. This work provides a path forward for future research investigating possible relationships between CFA demosaicing and color image super-resolution.