Currently, superconductor digital integrated circuits fabricated at HYPRES, Inc. can operate at clock frequencies approaching 40 GHz. The circuits present multilayered structures containing tens of thousands of Nb/Al/AlOx/Nb Josephson junctions (JJs) of various sizes interconnected by four Nb wiring layers, resistors, and other circuit elements. In order to be fully operational, the integrated circuits should be fabricated such that the critical currents of the JJs are within the tight design margins and the proper relationships between the critical currents of JJs of different sizes are preserved. We present experimental data and discuss mechanisms of process-induced variations of the critical current and energy gap of Nb/Al/AlOx/Nb JJs in integrated circuits. We demonstrate that the Josephson critical current may depend on the type and area of circuit elements connected to the junction, on the circuit pattern, and on the step in the fabrication process at which the connection is made. In particular, we discuss the influence of (a) the junction base electrode connection to the ground plane, (b) the junction counter electrode connection to the ground plane, and (c) the counter electrode connection to the Ti/Au or Ti/Pd/Au contact pads by Nb wiring. We show that the process-induced changes of the properties of Nb/Al/AlOx/Nb junctions are caused by migration of impurity atoms (hydrogen) between the different layers comprising the integrated circuits.