Thanks Michael and Mark for your excellent suggestions. I will look to incorporate them next time I attempt similar measurements.
The only one I am not convinced of is the effect of reciprocity failure. I would like to explain my reasoning so that you can point out the flaw if it is incorrect. My understanding is that the physics behind reciprocity failure is that the formation of a latent image center requires multiple photons. The intermediate states (latent pre-image centers) are unstable and as the time between photons increases, the chance that an intermediate state may return to its initial completely unexposed state increases. Since both the decay time of the pre-image center and the time between photons are randomly distributed, as the light level (average rate of photons) is decreased, there is a gradual loss of sensitivity due to the increased number of latent pre-image centers that decompose before they become stable latent image centers.
This means that for a given film illumination level, the rate of latent image center formation is constant irrespective of the shutter speed. If the illumination level is sufficiently high that the efficiency of latent image formation is close to optimum, then reciprocity failure will not be significant. If it does occur, then it effectively reduces the sensitivity of the film by a certain amount which is independent of the shutter speed. So provided the light intensity is the same for all exposures, the effect of any reciprocity failure would be simply to shift the curve on the (logarithmic) X axis.
By comparison, if I had kept the shutter speed constant and changed the illumination level (by varying the strength of the light source or adjusting the aperture) then the varying light levels on the film plane could have changed the efficiency of latent image formation, distorting the curve (since latent image formation would be more efficient at higher light levels and less efficient at lower light levels).
Because I was concerned about the possible effect of reciprocity failure, I measured it using similar technique prior to measuring the characteristic curve. I found that there is no effect (to within about 0.03 DU) at Zone V density for exposure times of up to (and including) 8 seconds. Of course this is really short-hand for saying there is no effect for light levels as low as that required to expose an ISO 100 film to Zone V level in 8 seconds because it is not the shutter speed, but the illumination level that determines the amount of reciprocity failure.
Since the illumination level I used to measure the characteristic curve was more than double this (3.2 seconds for zone V exposure), I concluded that reciprocity failure would be insignificant within the limits of my measurement capability (0.1 stops on the enlarger baseboard, which is 0.03 DU). The choice of illumination level was a compromise between light fall-off (which could be improved by stopping down both the enlarger lens and the camera lens) and reciprocity failure (which would be improved by opening up both the enlarger lens and the camera lens).
If you find a flaw in my reasoning, please let me know!