  Weak lensing provides an important route toward collecting samples of
clusters of galaxies selected by mass. Subtle systematic errors in image
reduction can compromise the power of this technique. We use the B-mode signal
to quantify this systematic error and to test methods for reducing this error.
We show that two procedures are efficient in suppressing systematic error in
the B-mode: (1) refinement of the mosaic CCD warping procedure to conform to
absolute celestial coordinates and (2) truncation of the smoothing procedure on
a scale of 10$^{\prime}$. Application of these procedures reduces the
systematic error to 20% of its original amplitude. We provide an analytic
expression for the distribution of the highest peaks in noise maps that can be
used to estimate the fraction of false peaks in the weak lensing $\kappa$-S/N
maps as a function of the detection threshold. Based on this analysis we select
a threshold S/N = 4.56 for identifying an uncontaminated set of weak lensing
peaks in two test fields covering a total area of $\sim 3$deg$^2$. Taken
together these fields contain seven peaks above the threshold. Among these, six
are probable systems of galaxies and one is a superposition. We confirm the
reliability of these peaks with dense redshift surveys, x-ray and imaging
observations. The systematic error reduction procedures we apply are general
and can be applied to future large-area weak lensing surveys. Our high peak
analysis suggests that with a S/N threshold of 4.5, there should be only 2.7
spurious weak lensing peaks even in an area of 1000 deg$^2$ where we expect
$\sim$ 2000 peaks based on our Subaru fields.
