Rats probably see a blurry world with faint greens, blues and ultraviolets. I've created movies of how the world may look through the eyes of a rat:
These movies are an informed interpretation of the scientific literature on rat vision, within the limits of current technology.
The biggest difference between the movies and actual rat vision is that rats have a much wider field of vision than we do. Therefore, rats see the world going by above and on either side of them as well as in front. But computer screens are flat, and humans have forward-facing eyes, so it would be very difficult to portray this on a flat screen. Any portrayal of panoramic vision on a flat surface would be greatly distorted. The best way to experience panoramic rat vision might be in an IMAX theater, which projects an enormously expanded field of view.
Regarding color, rats can distinguish ultraviolets, blues and greens. However, these color cues don't seem to be very meaningful to them: it takes rats a long time to be trained to discriminate these colors. In contrast, they can be trained to discriminate brightnesses pretty quickly. I interpret this to mean that rats can sense these colors, but these colors must be faint or the rats would use them naturally. To represent this, I reduced the color saturation down to a barely noticeable level.
Regarding blur, all the literature I've read agrees that rats have poor visual acuity. A recent paper put rat vision at about 20/600. I have 20/600 vision myself, so in the rat movie I matched the degree of blur in the movie to what I see without my corrective lenses.
Albino rats have extremely poor vision, estimated at 20/1200. To represent this I doubled the blur. The retinas of albino rats are flooded with light because their irises are translucent. This dazzling leads to gradual degeneration of the retina with exposure to ambient light. To simulate this dazzling I increased the lightness of the image.
To make the movie, I took a series of still photographs using a Kodak DC240 digital camera. I advanced the camera about 1 cm between each shot, and took a total of 148 photographs. In Photoshop, I edited the photos to approximate the rat's vision. To approximate red-green colorblindness, I changed the red channel to solid black, then copied and pasted the green channel into the red channel. To mimic the rat's faint perception of color, I reduced the color saturation of the image down to a just noticeable level (-70%). To mimic the rat's blurry vision, I applied a Gaussian blur (I have 20/600 vision myself, so I tried to match the amount of blur to what I see without corrective lenses). I used a Gaussian blur of 8 pixels (this blur looked right when the image size was subsequently reduced by 50% for the movie). Once the images were edited, I strung them together at 12 frames per second using a program called QuickMovie. To simulate the albino rat's vision, I reduced the color saturation by -80% and doubled the blur (Gaussian blur of16 pixels). I increased the lightness by 30% to simulate the light flooding through the iris to dazzle the retina. The "human cam" movie is made from the original set of unmodified photographs.