The water filter housing lower seal was mis-installed which allowed water to seep out and run down the housing case. Over time the water dropped onto a lavatory drain line, followed the line to a low point and collected on the stab aug computer box. The fluid accumulation resulted in corrosion on one of the circuit boards within the computer box causing a power imbalance within the yaw damper system and a subsequent uncommanded rudder signal. During the climb to cruise transition a Mach trim failure occurred which would have necessitated the use of the autopilot for speeds in excess of 0.7 Mach. Operation of the autopilot, however, resulted in operation of the yaw damper system which had been determined to have been producing uncommanded rudder inputs. As the aircraft was levelled at FL330 and the airspeed was allowed to exceed Mach 0.7 the copilot activated the autopilot which powered the malfunctioning damper system and a Dutch roll maneuver ensued. The PIC disconnected the autopilot, executed a descent and recovery.