1 mV is pretty small.

I would try uping my shunt to a .1 high wattage R.

The filter is a good idea agains the transients, so if you are using a 10K R for your series R to the A/D input, put a 1uF cap on the shunt side of this resistor. I would think that would be enought to smooth out the rough edges.

I would be checking this with an O-scope, just to verify that it is the problem.

A general purpose op-amp could be used to boost the signal up by a factor of 100 once you get the transients under control.

Also, check out ALLElectronics, I think they have a current donut pretty cheap.

Have fun
dw