  We analyze conditions for violation of the Bell inequality in the
Clauser-Horne-Shimony-Holt form, focusing on the Josephson phase qubits. We
start the analysis with maximum violation in the ideal case, and then take into
account the effects of the local measurement errors and decoherence. A special
attention is paid to configurations of the qubit measurement directions in the
pseudospin space lying within either horizontal or vertical planes; these
configurations are optimal in certain cases. Besides local measurement errors
and decoherence, we also discuss the effect of measurement crosstalk, which
affects both the classical inequality and the quantum result. In particular, we
propose a version of the Bell inequality which is insensitive to the crosstalk.
