This is an area quite a few process control engineers get wrong, but not through any fault of their own.
Differential inputs are usually employed when there is a very small signal that needs to be accurately read in a rather noisy or hostile environment. Their ability to 'ignore' any signal that appears, in phase and amplitude, on both the positive and negative input lines simultaneously is what gives the differential input its strength.
What is not taught is that this ability has its limits. In one email the writer explained that under certain conditions some inputs were starting to read high as well as become erratic. The give-away comment was when he said the input system was deliberately not earthed in any way so as to ensure there were no ground loops and relied solely on the input systems to provide such earthing.
Maybe it was a lack of understanding of how a differential input system works but there was a rather blinding error made in the statement - how was a balanced input system (both lines are inputs) going to provide a reasonable earthing point!? But he is not alone with this.
What goes wrong is the inputs only have a limited range before they approach overload. The difference may still be well within the accepted range, but will only be processed accurately if each input of the balanced pair is not overloaded in any way.
Such inputs have many subtle design changes and some may even have a sufficiently low impedance so as to keep any device attached to them well within operating limits. Higher impedance inputs cannot be as accommodating and is when issues arise. The worst case is the inputs may be operating very close to the limit and only exceeded at random intervals leading to a diagnosis of an intermittent fault.
The cure is relatively simple by ensuring that each and every portion of a system has an earth reference. If trying to ascertain if a fault on a plant is due to such an error then use a digital multimeter (an analogue one may present a low enough impedance to hide such voltages) and measure each input of a differential system to ensure the common-mode voltages are not exceeded (the manufacturer of the measuring system may have to be consulted for this).
Be sure to measure both AC and DC. Also remember to multiply AC voltages by 1.414 as the peak of an AC signal is this, and to then add this to the DC voltage (the overload may be a combination of both).