Recently i found the same problem with two HP 3437A system voltmeters that we have. After one of them showed occasional digital errors (e.g. failure of display multiplexer) i looked inside. While the power supply generated 4.9 V at 1.5 A, some corners of the digital board received only 4.73 V or so, with a large part of the loss along the ground network. I just added two wires (Gnd and +5V) from one corner to the opposite one as redundant connection and the losses are less than 20 or 30 mV now. The faults are gone.
The digital boards of that time had very few buffer caps. In the 3437A i measured up to 1 Vpp noise on the +5 V net. When looking at the 3456A digital boards (especially those with CMOS logic) i am missing buffer caps that are so common nowadays, especially near the isolation interface digital receivers.
Regards, Dieter