  We attempt to measure possible miscalibration of the wavelength scale of the
VLT-UVES spectrograph. We take spectra of QSO HE0515-4414 through the UVES
iodine cell which contains thousands of well-calibrated iodine lines and
compare these lines to the wavelength scale from the standard thorium-argon
pipeline calibration. Analyzing three exposures of this z = 1.71 QSO, we find
two distinct types of calibration shifts needed to correct the Th/Ar wavelength
scale. First, there is an overall average velocity shift of between 100 m/s and
500 m/s depending upon the exposure. Second, within a given exposure, we find
intra-order velocity distortions of 100 m/s up to more than 200 m/s. These
calibration errors are similar to, but smaller than, those found earlier in the
Keck HIRES spectrometer. We discuss the possible origins of these two types of
miscalibration. We also explore the implications of these calibration errors on
the systematic error in measurements of the relative change in alpha (current
value - past value) / current value, the change in the fine-structure constant
derived from accurate measurement of the relative redshifts of absorption lines
in QSO absorption systems. The overall average, exposure-dependent shifts
should be less relevant for fine-structure work, but the intra-order shifts
have the potential to affect these results. Using either our measured
calibration offsets or a Gaussian model with sigma of around 90 m/s, Monte
Carlo mock experiments find errors in the relative change in alpha of between
1e-6 Nsys^(-1/2) and 3e-6 Nsys^(-1/2), where Nsys is the number of systems used
and the range is due to dependence on how many metallic absorption lines in
each system are compared.
