  We measure the Shubnikov-de Haas effect in thin-film Sr$_2$RuO$_4$ grown on
an (LaAlO$_3$)$_{0.29}$-(SrAl$_{1/2}$Ta$_{1/2}$O$_3$)$_{0.71}$ (LSAT)
substrate. We detect all three known Fermi surfaces and extract the Fermi
surface volumes, cyclotron effective masses, and quantum lifetimes. We show
that the electronic structure is nearly identical to that of single-crystal
Sr$_2$RuO$_4$, and that the quasiparticle lifetime is consistent with the Tc of
comparably clean, single-crystal Sr$_2$RuO$_4$. Unlike single-crystal
Sr$_2$RuO$_4$, where the quantum and transport lifetimes are roughly equal, we
find that the transport lifetime is $1.3\pm0.1$ times longer than the quantum
lifetime. This suggests that extended (rather than point) defects may be the
dominant source of quasiparticle scattering in these films. To test this idea,
we perform cross-sectional STEM and find that out-of-phase boundaries extending
the entire thickness of the film occur with a density that is consistent with
the quantum mean free path. The long quasiparticle lifetimes make these films
ideal for studying the unconventional superconducting state in Sr$_2$RuO$_4$
through the fabrication of devices -- such as planar tunnel junctions and
SQUIDs.
