  We present new results from extremely deep, high-resolution images of the
field around the double quasar QSO 0957+561. A possible gravitational arc
system near the double quasar has recently been reported, which, if real, would
set strong constraints on determinations of the Hubble constant from the time
delay in the double quasar. We find that both the morphology and the colors of
the claimed arc systems suggest that they are chance alignments of three and
two different objects, and not gravitationally lensed arcs. Hence, the
constraints on $H_0$-determinations from the arcs are not valid. Also, a small
group of galaxies at $z=0.5$ near the line-of-sight which was required to have
a very large mass in the physically interesting arc models, is most likely
insignificant. From our deep images we are able to use weak lensing of faint
background galaxies in the field to map the gravitational potential in the main
cluster. This sets new constraints on determinations of $H_0$. We find that the
Hubble constant is constrained to be less than 70km/(s Mpc), if the time delay
between the two images of the QSO is equal to or larger than 1.1 years.
