The primary logistical obstacles to an account such as the one found in Genesis have concerned the mechanics of accounting for every species. However, given the reality of speciation (Christians need object only to theories of common ancestry, which is a logically distinct body of hypotheses), there is no reason to think that the original number of species could not have been much smaller than it is now (thus minimizing and perhaps eliminating the alleged difficulty). As for the other spheres relevant to this question (geological, meteorological, etc.), the evidence on this front is multi-faceted and interesting, and will be explored in the coming weeks.
You may also be interested in Noah's Flood: A Bird's-Eye View and
Exploring The Extent of the Flood - Part I