Explore Evolution's arguments against molecular clocks are a bungled mishmash of actual facts, misinterpretations and completely spurious claims. First, the authors raise the issue of calibration of the molecular clock. This is an acknowledged potential problem in using the clock to date certain evolutionary events, especially those in the very deep past. Nevertheless, when appropriate methodology and controls are used, molecular clock dating has been shown to be reliable and consistent.
Contrary to the authors' statement, "environmental factors" such as magnetic field changes and mass extinctions are thought to play a minor role, at best, in molecular clock variation, as opposed to intrinsic differences in generation times/molecular substitution rates and selective forces across lineages and time. Significantly, the author's use and misattribution of this "environmental factors" claim appears to have resulted from their reliance on secondary creationist sources, instead of the primary scientific literature they cite.
Regardless of the claims in Explore Evolution, common ancestry is not dependent on any particular molecular clock. At best, this is again dependent on creationist sources. At worst, it is simply irrelevant.