Very important is to first look at the hardware-design of the board. Is there a possibility that the noise is generated by the board itself or are the inputs resposible for the noise. In the first case you should observe things like power-supply and -also very important- the prescense of all the right pull-ups/down for the signals to be read. Another thing is: are all chips decoupled at their supply by a capacitor of at least 10nF? Is the power supply steady and does it have less than say 5% ripple?.
After checking all this, look at the power-traces, are they strong enough to cary the current to the chips without producing ripple by themselves?
If this all seems OK then you could observe the inputs closer. Is the power-supply feeding the commons of the inputs strong enough and stabilized? Perhaps it is nescessary to filter the inputs or use a stronger pull-up/down resistor.

good luck