|Zebu cattle (Bos taurus indicus)|
Agricultural Research Service (USDA) Public Domain
The answer is 6495 species and counting. Compared to Wilson & Reeder Mammal Species of the World (MSW3), which has its own database (here), that is an increase of 1250 in 13 years.
The authors of ASM MDD have erred in favour of the splitters. In particular, acceptance of the taxonomy of Groves & Grubb for Artiodactyla and Perissodactyla (previous post) will raise eyebrows. In anticipation they write, "inclusion of the taxonomy of Groves and Grubb (2011) in the MDD ensures that these taxa are vetted by the greater mammalogical community."
I note, however, that unlike Castello (previous post), they list the zebu as a subspecies of Bos taurus. Important because this species is a focus in research on bovine placentation and reproduction in places like Brazil.
I found the new MDD more difficult to navigate than MSW3. For example, if you enter a higher taxon than genus you get all the entries in that taxon rather than any definition of the Family or Order itself.
As far as I can see there is no possibility to search for synonyms as on MSW3. I have found this search function of MSW3 enormously valuable when delving into the older literature on placentation. Similarly there is little information about subspecies names.
Some choices of terminology meet my approval. They drop Cetartiodactyla in favour of Artiodactyla (whales and their kin are nested within even toed ungulates). Inevitably they retain Afrosoricida for the order that includes tenrecs, otter shrews and golden moles (a really unfortunate name as African shrews are numerous and belong to an entirely different clade).
Most regrettaby, however, they retain Infraclass Placentalia for eutherians. This unfortunate term was introduced by McKenna & Bell and I have ranted about it before (previous post). It has caused countless confusion and the vernacular "placentals" or even "placental mammals" can mislead the unwary to believe marsupials are without placentation. Prothero among them (previous post).