  Charge and spin current correlations are analyzed in a source of
spin-entangled electrons built from a superconductor and two quantum dots in
parallel. In addition to the ideal (crossed Andreev) channel, parasitic
channels (direct Andreev and cotunneling) and spin flip processes are fully
described in a density matrix framework. The way they reduce both the
efficiency and the fidelity of the entangler is quantitatively described by
analyzing the zero-frequency noise correlations of charge current as well as
spin current in the two output branches. Spin current noise is characterized by
a spin Fano factor, equal to 0 (total current noise) and -1 (crossed
correlations) for an ideal entangler. The violation of the Bell inequalities,
as a test of non-locality (entanglement) of split pairs, is formulated in terms
of the correlations of electron charge and spin numbers counted in a specific
time window $\tau$. The efficiency of the test is analyzed, comparing $\tau$ to
the various time scales in the entangler operation.
