Spikes - DC Motor Current Sensing
Commutation noise caused by the brushes making and breaking connection as the rotor spins. 



Usually filtered using a snubber RC arrangement like this...



Or if you are really clever you can actually channel that noise as motor speed feedback.

The fact that you are measuring the current after the switch probably is not helping you either... Those high or low side diff amps are really meant to have at least one side of the shunt at a fixed potential. I suggest you move it up to the VM line.