We present a detailed examination of the heavy flavor content of the W + jet sample collected with the CDF detector. Jets containing heavy flavor quarks are selected via the identification of secondary vertices or semileptonic decays of b and c quarks. There is generally good agreement between the rates of secondary vertices and soft leptons in the data and in the standard model simulation including single and pair production of top quarks. An exception is the number of events in which a single jet has both a soft lepton and a secondary vertex tag. In W + 2,3 jet data, we find 13 such events where we expected 4.4 +- 0.6 events. The kinematic properties of this small sample of events are statistically difficult to reconcile with the simulation of standard model processes. Several phenomenological approaches are used to model these data and to estimate their production cross section.