  Many photometric time-domain surveys are driven by specific goals, such as
searches for supernovae or transiting exoplanets, which set the cadence with
which fields are re-imaged. In the case of the Palomar Transient Factory (PTF),
several sub-surveys are conducted in parallel, leading to non-uniform sampling
over its $\sim$$20,000 \mathrm{deg}^2$ footprint. While the median $7.26
\mathrm{deg}^2$ PTF field has been imaged $\sim$40 times in \textit{R}-band,
$\sim$$2300 \mathrm{deg}^2$ have been observed $>$100 times. We use PTF data to
study the trade-off between searching for microlensing events in a survey whose
footprint is much larger than that of typical microlensing searches, but with
far-from-optimal time sampling. To examine the probability that microlensing
events can be recovered in these data, we test statistics used on uniformly
sampled data to identify variables and transients. We find that the von Neumann
ratio performs best for identifying simulated microlensing events in our data.
We develop a selection method using this statistic and apply it to data from
fields with $>$10 $R$-band observations, $1.1\times10^9$ light curves,
uncovering three candidate microlensing events. We lack simultaneous,
multi-color photometry to confirm these as microlensing events. However, their
number is consistent with predictions for the event rate in the PTF footprint
over the survey's three years of operations, as estimated from near-field
microlensing models. This work can help constrain all-sky event rate
predictions and tests microlensing signal recovery in large data sets, which
will be useful to future time-domain surveys, such as that planned with the
Large Synoptic Survey Telescope.
