Mucky cords: as long as you clean them with the power off, you should do fine. BrakeClean is a decent solvent BUT it may remove labels or some ink identifiers. Wipe the wires down with paper towels to get big muck/oil off them and then give them a shot with brake clean.
Motor hunting/buzzing issues: the motors can "hunt" when idle if the tune is off. My understanding is that the servo gain is asking for so little correction to achieve the position that the thing is buzzing back and forth. That or else it is asking for correction that essemtially isn't need which is why it "hunts"
The tach and encoder won't pick up on it if it is merely buzzing as the motor probably hasn't rotated enough to either create a tach signal or made enough of an encoder change to generate a corretion requirement.
How you adjust/tune the amp depends on who's amp it is. Ditto that for the tools needed to adjust. In some instances, a voltmeter is all that's needed. In others, you may need an oscilloscope. In some Bridgeports, there is a tuning program that will endable you to effectively tune the servos while in DOS and not every turn a pot on the amps.
You should hope that Machintek picks up on this thread - he's the expert in the servo tuning dept and if anybody has insight, he should.