The image size increases linearly with respect to distance between the pinhole and the film plane. The image gets larger in all dimensions.
The image gets sharper as you increase the distance between the pinhole and the film plane, but after a point, the effects of diffractions become important, so here is an optimum pinhole size (alternatively, for a given pinhole, there is an optimum imaging distance).
Light intensity at the film plane decreases with the square of the distance between the pinhole and the film plane, so you need to increase exposure. This is equivalent to normal photography, however, as the amount of gathered light is proportional with the square of the pinhole. The usual concept of aperture (f/D) as a factor in exposure is the same, just that the iris is replaced by the pinhole and the focal length is replaced by the distance between the pinhole and the film plane.
Since exposures will probably be long, you probably need to take into account reciprocity failure.