  We investigate the occurrence of multiple weak deflections in deep data sets
which are used to detect galaxy-galaxy lensing. Using the galaxies in the HDF
(North) for which both redshifts and rest-frame blue luminosities are known, we
show that the probability for a given source galaxy to be lensed by two or more
foreground galaxies exceeds 50% for z_s > 1, and for which the separate,
individual deflections yield gamma > 0.005. Neglecting multiple deflections
when obtaining best-fitting halo parameters for the lens galaxies can lead to
an overestimate by a factor of order 2 for the halo mass interior to a radius
of 100 kpc/h. We also show that multiple weak deflections create systematic
effects which may hinder observational efforts to use weak lensing to constrain
the projected shapes of the halos of field galaxies. For a data set in which
the galaxies have magnitudes in the rage 19 < I < 23, multiple deflections
result in strong correlations between the post-lensing image shapes of most
foreground-background pairs of galaxies. Imposing a simple redshift cut during
the data anaysis is sufficient to reduce the correlation between the final
images of lenses and sources to the point that the expected anisotropy in the
weak lensing signal can be detected via a straightforward average. We conclude
that previous theoretical calculations of weak lensing due to flattened halos
have considerably underestimated the sizes of the observational data sets which
would be required to detect this effect. [Abridged]
