  We critically examine issues associated with determining the fundamental
properties of the black hole and the surrounding accretion disk in an X-ray
binary based on modeling the disk X-ray continuum of the source. We base our
work mainly on two XMM-Newton observations of GX 339-4, because they provided
high-quality data at low energies (below 1 keV) which are critical for reliably
modeling the spectrum of the accretion disk. A key issue examined is the
determination of the so-called "color correction factor", which is often
empirically introduced to account for the deviation of the local disk spectrum
from a blackbody (due to electron scattering). This factor cannot be
pre-determined theoretically because it may vary with, e.g., mass accretion
rate, among a number of important factors. We follow up on an earlier
suggestion to estimate the color correction observationally by modeling the
disk spectrum with saturated Compton scattering. We show that the spectra can
be fitted well and the approach yields reasonable values for the color
correction factor. For comparison, we have also attempted to fit the spectra
with other models. We show that even the high-soft-state continuum (which is
dominated by the disk emission) cannot be satisfactorily fitted by
state-of-the-art disk models. We discuss the implication of the results.
