Residual flux conductivity on PCBs causing problems?
I have seen issues with no clean fluxes when doing very high impedance stuff (10G Ohm), judicious application of solvents and an ultrasonic cleaner cleared it up, IIRC the solvent was just IPA so no real need for anything particularly aggressive. Words were had with the assembly house and the problem never reappeared. 

The ones to Really watch are the water washable fluxes, which are fine if they manage to get them all off, but tend to be bad news if left on the board, I had problems with this on a high voltage assembly.