We have used Monte Carlo simulations to study the effects of nanotube alignment and measurement direction on the resistivity in single-walled carbon nanotube films. These films consist of multiple layers of conductive nanotube networks with percolative transport as the dominant conduction mechanism. We find that minimum resistivity occurs for a partially aligned rather than a perfectly aligned nanotube film. When nanotubes are strongly aligned, the film resistivity becomes highly dependent on the measurement direction. We also find that aligning the nanotubes too strongly or measuring the resistivity in a direction which is very different from the alignment direction causes the film to approach the percolation threshold, as evidenced by the inverse power law increase in resistivity. Furthermore, the location of the resistivity minimum and the values of the inverse power law critical exponents are not universal, but depend strongly on other nanotube and device parameters. To illustrate this explicitly, we have studied the effect of three parameters, namely, nanotube length, nanotube density per layer, and device length on the scaling of nanotube film resistivity with nanotube alignment and measurement direction. We find that longer nanotubes, denser films, and shorter device lengths decrease the alignment critical exponent and the alignment angle at which minimum resistivity occurs, but increase the measurement direction critical exponent. However, the amount of increase or decrease in the critical exponents or the minima locations is different for each parameter. We explain these results by simple physical and geometrical arguments. Characterizing and understanding the effects of alignment and measurement direction on the percolation resistivity in films and composites made up of one-dimensional conductors, such as nanotubes, give valuable insights into the optimal way to arrange these nanomaterials for potential applications in optoelectronics, sensors, and flexible microelectronics.