Still I was confused because I thought he was trying to compare the same feature (an absorption (usually) or emission line) in wavelength space but the data weren't taken at the same central wavelengths at all. There was hardly any overlap. It turned out he was not comparing the same feature but different features in redshift space, not wavelength space. Redshift is the amount a feature moves in wavelength or velocity, etc. due to the fact that it is moving away from us. This relates to something you may have heard of called the Doppler effect? It is expressed in terms of "delta lambda over lambda" which is equal to "v over c". Lambda (the Greek letter lambda) stands for the rest wavelength, where you expect to find the feature if it weren't moving away from you. Delta lambda is the difference in wavelength between where you found the object and the rest wavelength. "v" is velocity, the speed at which it is moving away. And "c" is, of course, the speed of light.
The General Observer) was plotting his lines of different wavelength on a redshift (or velocity) scale, then trying to fit them with theoretical profiles. What he found was that the absorption lines in the March 94 data line up at the same redshift, but the line in the October 95 data appear to be at a slightly different redshift. And that is the shift he didn't understand. But I figured out that the wavelength calibration has changed since the first data were taken. It is quite possible, probable, and hopeful that if he recalibrates his data the unexpected shift will go away.
Of course, while I am working on this problem, I also have several more that I am trying to keep on top of...but my ability or lack of ability to do more than one chore at a time is the topic for another journal.