Anybody read "emperor of ocean park?" Part of the plot turns on whether two dark spots in an autopsy photo are bullets or dust on the lens. Hah !!! One of two plot errors I've seen in an otherwise excellent book.
The invisibility of the spot-on-the-lens is because the spot is so far out of focus that it's circle of confusion is larger than the image. Nonetheless, the image of the spot is indeed spread out over the entire sensor, resulting in a loss of contrast. As petkal drools more pea soup onto his lenses, the fraction of the image on the sensor from out-of-focus objects on the lens increases, and image quality goes down.
Mike and Lester are quite right - a lens with narrow depth-of-field can shoot thru a close chain link fence. You just get a loss of contrast, due to the blurred out contribution from the fence.
Peter, a better nursing attendant would mop up the pea-soup before the drool departs from your chin, helping to keep your lenses clean. Look into it.