  Orbital, spin and astrometric parameters of the millisecond pulsar PSR
J0621+1002 have been determined through six years of timing observations at
three radio telescopes. The chief result is a measurement of the rate of
periastron advance, omega_dot = 0.0116 +/- 0.0008 deg/yr. Interpreted as a
general relativistic effect, this implies the sum of the pulsar mass, m_1, and
the companion mass, m_2, to be M = m_1 + m_2 = 2.81 +/- 0.30 msun. The
Keplerian parameters rule out certain combinations of m_1 and m_2, as does the
non-detection of Shapiro delay in the pulse arrival times. These constraints,
together with the assumption that the companion is a white dwarf, lead to the
68% confidence maximum likelihood values of m_1 = 1.70(+0.32 -0.29) msun and
m_2 =0.97(+0.27 - 0.15) msun and to the 95% confidence maximum likelihood
values of m_1 = 1.70(+0.59 -0.63) msun and m_2 = 0.97(+0.43 -0.24) msun. The
other major finding is that the pulsar experiences dramatic variability in its
dispersion measure (DM), with gradients as steep as 0.013 pc cm^{-3} / yr. A
structure function analysis of the DM variations uncovers spatial fluctuations
in the interstellar electron density that cannot be fit to a single power law,
unlike the Kolmogorov turbulent spectrum that has been seen in the direction of
other pulsars. Other results from the timing analysis include the first
measurements of the pulsar's proper motion, mu = 3.5 +/- 0.3 mas / yr, and of
its spin-down rate, dP/dt = 4.7 x 10^{-20}, which, when corrected for kinematic
biases and combined with the pulse period, P = 28.8 ms, gives a characteristic
age of 1.1 x 10^{10} yr and a surface magnetic field strength of 1.2 x 10^{9}
G.
