There are two nice treatments of the data problem which come to very similar conclusions. They both benefit from re-analyzing the data themselves, which I have not done. This weekend I've taken the easy way out and criticized the work of others. One thing these two authors note is that, contrary to what I said below, the Berkeley results are driven by two large Dem-leaning counties, Broward and Palm Beach. That means the phenomenon is almost certainly not due to characteristics of electronic voting but to characteristics of these two counties, and not necessarily nefarious characteristics, either.
Kieran Healey, a sociologist at the University of Arizona, shows that if one were to include a dummy variable for those two counties, the electronic voting effects are washed out. Thus, the focus of our inquiry, if there is one, ought to be on why these two swung for Bush.
Andrew Gelman, a statistician at Columbia who has published quite a bit on electoral behavior, reaches an identical conclusion. He also has some nice illustrative graphs to show the influence of Broward and Palm Beach on the Berkeley team's regression results. He points out that it would be a leap to say there were shenanigans in these two counties; instead, there may have been quirks of turnout, demographics, political leanings or something else which might have increased the Bush vote there. After all, the magnitude of change is not unreasonably large by historical standards.