Why is there a capacitor that is parallel to Op Amp inputs in this circuit?
The capacitor is to prevent a DC bias shift from being caused by EMI. Bipolar op-amps in particular can act as "detectors" to RF signals, and the capacitor shunts the RF to reduce the amplitude ( at the expense of increasing noise and reducing phase margin ) so it should not be too large a value capacitor.

Although all the parts are close together with minimum lead length, one could expect there is a major source of EMI nearby in the switching power supply.