Changing noise level with 24-Bit A/D Converter
One amp at 60Hz has dI/dT of 377 amps/second.

If that, modeled as a SINGLE INFINITE WIRE, is 1 meter from your differential inputs, those +/- wires running 1meter with 1cm separation, we compute the magnetically-induced differential noise as

Vinduce = [ 2e-7 * Area/Distance ] * dI/dT

Inserting numbers, we have

Vinduce = 2e-7 * (1meter * 1cm)/1meter * 377 amp/secod

Vinduce = 2e-7 * 1cm * 377 = 0.754 microVolts

without ANY powerline spikes from motors or microwave ovens, etc. Microwave ovens easily increase this dI/dT (the 377) by 1,000X or 10,000X, and you would have 7 millivolts of trash.
Using twisted pair might drop the interference by 10X, to 700 microVolts of trash.