  The POINT-AGAPE collaboration is currently searching for massive compact halo
objects (MACHOs) towards the Andromeda galaxy (M31). The survey aims to exploit
the high inclination of the M31 disk, which causes an asymmetry in the spatial
distribution of M31 MACHOs. Here, we investigate the effects of halo velocity
anisotropy and flattening on the asymmetry signal using simple halo models. For
a spherically symmetric and isotropic halo, we find that the underlying
pixel-lensing rate in far-disk M31 MACHOs is more than 5 times the rate of
near-disk events. We find that the asymmetry is increased further by about 30%
if the MACHOs occupy radial orbits rather than tangential orbits, but is
substantially reduced if the MACHOs lie in a flattened halo. However, even for
haloes with a minor-to-major axis ratio q = 0.3, the numbers of M31 MACHOs in
the far-side outnumber those in the near-side by a factor of ~2. We show that,
if positional information is exploited in addition to number counts, then the
number of candidate events required to confirm asymmetry for a range of
flattened and anisotropic halo models is achievable, even with significant
contamination by variable stars and foreground microlensing events. For
pixel-lensing surveys which probe a representative portion of the M31 disk, a
sample of around 50 candidates is likely to be sufficient to detect asymmetry
within spherical haloes, even if half the sample is contaminated, or to detect
asymmetry in haloes as flat as q = 0.3 provided less than a third of the sample
comprises contaminants. We also argue that, provided its mass-to-light ratio is
less than 100, the recently observed stellar stream around M31 is not
problematic for the detection of asymmetry. (Abstract slightly abridged.)
