  Ideal monolayers of common semiconducting transition metal dichalcogenides
(TMDCs) such as MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$ possess many similar
electronic properties. As it is the case for all semiconductors, however, the
physical response of these systems is strongly determined by defects in a way
specific to each individual compound. Here we investigate the ability of
exfoliated monolayers of these TMDCs to support high-quality, well-balanced
ambipolar conduction, which has been demonstrated for WS$_2$, MoSe$_2$, and
WSe$_2$, but not for MoS$_2$. Using ionic-liquid gated transistors we show
that, contrary to WS$_2$, MoSe$_2$, and WSe$_2$, hole transport in exfoliated
MoS$_2$ monolayers is systematically anomalous, exhibiting a maximum in
conductivity at negative gate voltage (V$_G$) followed by a suppression of up
to 100 times upon further increasing V$_G$. To understand the origin of this
difference we have performed a series of experiments including the comparison
of hole transport in MoS$_2$ monolayers and thicker multilayers, in exfoliated
and CVD-grown monolayers, as well as gate-dependent optical measurements (Raman
and photoluminescence) and scanning tunneling imaging and spectroscopy. In
agreement with existing {\it ab-initio} calculations, the results of all these
experiments are consistently explained in terms of defects associated to
chalcogen vacancies that only in MoS$_2$ monolayers -- but not in thicker
MoS$_2$ multilayers nor in monolayers of the other common semiconducting TMDCs
-- create in-gap states near the top of the valence band that act as strong
hole traps. Our results demonstrate the importance of studying systematically
how defects determine the properties of 2D semiconducting materials and of
developing methods to control them.
