Glitchy pulses in a data acquisition system
Clearly you have a serious EMI problem on your MUX selector causing it to switch channels erroneously.  




If you do not know how to measure signal integrity of each interface signal both input and output with a scope, then you have to blindly start filtering and shielding with CM chokes , shielded cable and Low Pass filters to lower the source impedance for rejecting Stray EMI either ground conducted or radiated.


this should be trivial to fix for an "analog" engineer with 1yr of RF experience.