  We present a newly implemented single-pulse pipeline for the PALFA survey to
efficiently identify single radio pulses from pulsars, Rotating Radio
Transients (RRATs) and Fast Radio Bursts (FRBs). We have conducted a
sensitivity analysis of this new pipeline in which multiple single pulses with
a wide range of parameters were injected into PALFA data sets and run through
the pipeline. Based on the recovered pulses, we find that for pulse widths $\rm
< 5\ ms$ the sensitivity of the PALFA pipeline is at most a factor of $\rm \sim
2$ less sensitive to single pulses than our theoretical predictions. For pulse
widths $\rm > 10\ ms$, as the $\rm DM$ decreases, the degradation in
sensitivity gets worse and can increase up to a factor of $\rm \sim 4.5$. Using
this pipeline, we have thus far discovered 7 pulsars and 2 RRATs and identified
3 candidate RRATs and 1 candidate FRB. The confirmed pulsars and RRATs have DMs
ranging from 133 to 386 pc cm$^{-3}$ and flux densities ranging from 20 to 160
mJy. The pulsar periods range from 0.4 to 2.1 s. We report on candidate FRB
141113, which we argue is likely astrophysical and extragalactic, having $\rm
DM \simeq 400\ pc~cm^{-3}$, which represents an excess over the Galactic
maximum along this line of sight of $\rm \sim$ 100 - 200 pc cm$^{-3}$. We
consider implications for the FRB population and show via simulations that if
FRB 141113 is real and extragalactic, the slope $\alpha$ of the distribution of
integral source counts as a function of flux density ($N (>S) \propto
S^{-\alpha}$) is $1.4 \pm 0.5$ (95% confidence range). However this conclusion
is dependent on several assumptions that require verification.
