  (abridged) We study the accuracy of various approximations to cosmic shear
and weak galaxy-galaxy lensing and investigate effects of Born corrections and
lens-lens coupling. We use ray-tracing through the Millennium Simulation to
calculate various cosmic-shear and galaxy-galaxy-lensing statistics. We compare
the results from ray-tracing to semi-analytic predictions. We find: (i) The
linear approximation provides an excellent fit to cosmic-shear power spectra as
long as the actual matter power spectrum is used as input. Common fitting
formulae, however, strongly underestimate the cosmic-shear power spectra. Halo
models provide a better fit to cosmic shear-power spectra, but there are still
noticeable deviations. (ii) Cosmic-shear B-modes induced by Born corrections
and lens-lens coupling are at least three orders of magnitude smaller than
cosmic-shear E-modes. Semi-analytic extensions to the linear approximation
predict the right order of magnitude for the B-mode. Compared to the
ray-tracing results, however, the semi-analytic predictions may differ by a
factor two on small scales and also show a different scale dependence. (iii)
The linear approximation may under- or overestimate the galaxy-galaxy-lensing
shear signal by several percent due to the neglect of magnification bias, which
may lead to a correlation between the shear and the observed number density of
lenses. We conclude: (i) Current semi-analytic models need to be improved in
order to match the degree of statistical accuracy expected for future
weak-lensing surveys. (ii) Shear B-modes induced by corrections to the linear
approximation are not important for future cosmic-shear surveys. (iii)
Magnification bias can be important for galaxy-galaxy-lensing surveys.
