Noise due to stray voltages in a data acquisition system
This question and answer explains how the output of many two-pronged AC (earthless) SMPSs use a capacitor internally to reduce excessive output switching noise because of internal transformer capacitive coupling.: -



The side effect is that both DC output terminals (open circuit) are "wobbled" around at the AC power frequency. It is harmless to humans but might cause a problem to some inputs of some DAQ boards.


  The data-acquisition max input voltage is +-10VDC. Would this stray
  voltage be problem in this case? Is it exceeding maximum common mode
  range?


You'd need to look at the data sheet of the DAQ card to see if it might be a problem.


  Is this configuration is more susceptible to error in readings than in
  differential ended inputs?


Yes it is, The use of an unbalanced input means that there will be more current flowing to earth from the interfering common-mode signal than what is flowing down the signal line and this might create a differential interfering signal of low-ish size.


  How would diff ended. connection eliminate the noise caused by stray
  voltages?


The input impedance to ground presented by both differential inputs is equal so, what was mentioned previously about imbalanced currents isn't applicable HOWEVER, if those impedances are high and no external capacitances are applied to suppress the common-mode voltage you could easily swamp the common-mode input range of the DAQ's differential input.