The organization of animals into groups such as families, genera, and species is (ever since Darwin) intended to reflect evolutionary history. As new creatures are discovered and old groupings studied more closely and with new techniques, the scientific community's understanding of evolutionary relationships continually changes in what is hoped to be a gradual refinement towards the truth. At any given time, there is some disagreement among authorities about, for example, which genera certain species belong in. So any taxonomical classification, including the one I've used on my site, is likely to be at least mildly controversial — some of the scientific names will be disputed by some researchers, and some will undoubtedly change with time.
Common English names are considerably less accepted and stable than scientific names. For this reason, I've listed multiple common names for many species.
It is impractical for most people (including myself) to keep up with the detailed literature on each species or group, so we usually rely on published overviews. For North American species, I'm using the Society for the Study of Amphibians and Reptiles names book as the authority for both scientific and common English names. A competitor is Joseph Collins's alternate taxonomy and names, which is published on-line by The Center for North American Herpetology.
Outside North America there is even less agreement. The worldwide list of scientific & common names published by Frank and Ramus, two non-herpetologists, was a remarkable achievement, but is not universally accepted among the herpetological community. I've tried to use it only when I couldn't find any more scientific reference. Of course, I have access to only a tiny fraction of the herpetological literature, and I am not myself a herpetologist.
Basically, you should take everything I say as the reasonably informed opinion of a very interested amateur.
An extremely useful reference for reptile classification is the on-line Reptile Database maintained by Peter Uetz and Jakob Hallermann.
Ellin Beltz has a marvelous site that explains the origins and meanings of the scientific names of North American amphibians and reptiles.