  Using several cosmological observations, i.e. the cosmic microwave background
anisotropies (WMAP), the weak gravitational lensing (CFHTLS), the measurements
of baryon acoustic oscillations (SDSS+WiggleZ), the most recent observational
Hubble parameter data, the Union2.1 compilation of type Ia supernovae, and the
HST prior, we impose constraints on the sum of neutrino masses ($\mnu$), the
effective number of neutrino species ($\neff$) and dark energy equation of
state ($w$), individually and collectively. We find that a tight upper limit on
$\mnu$ can be extracted from the full data combination, if $\neff$ and $w$ are
fixed. However this upper bound is severely weakened if $\neff$ and $w$ are
allowed to vary. This result naturally raises questions on the robustness of
previous strict upper bounds on $\mnu$, ever reported in the literature. The
best-fit values from our most generalized constraint read
$\mnu=0.556^{+0.231}_{-0.288}\rm eV$, $\neff=3.839\pm0.452$, and
$w=-1.058\pm0.088$ at 68% confidence level, which shows a firm lower limit on
total neutrino mass, favors an extra light degree of freedom, and supports the
cosmological constant model. The current weak lensing data are already helpful
in constraining cosmological model parameters for fixed $w$. The dataset of
Hubble parameter gains numerous advantages over supernovae when $w=-1$,
particularly its illuminating power in constraining $\neff$. As long as $w$ is
included as a free parameter, it is still the standardizable candles of type Ia
supernovae that play the most dominant role in the parameter constraints.
