  We present a new photometric catalog of 326 candidate globular clusters (GCs)
in the nearby spiral galaxy M101, selected from B, V, and I Hubble Space
Telescope Advanced Camera for Surveys images. The luminosity function (LF) of
these clusters has an unusually large number of faint sources compared with
GCLFs in many other spiral galaxies. Accordingly, we separate and compare the
properties of "bright" (M_V < -6.5) versus "faint" (M_V > -6.5; one magnitude
fainter than the expected GC peak) clusters within our sample. The LF of the
bright clusters is well fit by a peaked distribution similar to those observed
in the Milky Way (MW) and other galaxies. These bright clusters also have
similar size (r_{eff}) and spatial distributions as MW GCs. The LF of the faint
clusters, on the other hand, is well described by a power law, dN(L_V)/dL_V
proportional to L_V^alpha with alpha = -2.6 plus or minus 0.3, similar to those
observed for young and intermediate-age cluster systems in star forming
galaxies. We find that the faint clusters have larger typical r_{eff} than the
bright clusters, and have a flatter surface density profile, being more evenly
distributed, as we would expect for clusters associated with the disk. We use
the shape of the LF and predictions for mass-loss driven by two-body relaxation
to constrain the ages of the faint clusters. Our results are consistent with
two populations of old star clusters in M101: a bright population of halo
clusters and a fainter, possibly younger, population of old disk clusters.
