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We present radio transient search algorithms, results, and statistics from the ongoing Arecibo Pulsar ALFA (PALFA) survey of the Galactic plane. We have discovered seven objects through a search for isolated dispersed pulses. All of these objects are Galactic and have measured periods between 0.4 and 4.7 s. One of the new discoveries has a duty cycle of 0.01%, smaller than that of any other radio pulsar. We discuss the impact of selection effects on the detectability and classification of intermittent sources, and compare the efficiencies of periodicity and single-pulse (SP) searches for various pulsar classes. For some cases we find that the apparent intermittency is likely to be caused by off-axis detection or a short time window that selects only a few bright pulses and favors detection with our SP algorithm. In other cases, the intermittency appears to be intrinsic to the source. No transients were found with DMs large enough to require that they originate from sources outside our Galaxy. Accounting for the on-axis gain of the ALFA system, as well as the low gain but large solid-angle coverage of far-out sidelobes, we use the results of the survey so far to place limits on the amplitudes and event rates of transients of arbitrary origin.

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