The pilots’ failure to execute a go-around when the nighttime autopilot-coupled approach became unstable, which resulted in a loss of control and subsequent impact with terrain. Also causal was the flight instructor's inadequate supervision of the pilot and his failure to perform remedial action. Contributing to the accident was the inadvertent application of pressure to the pitch control while the autopilot was engaged, which caused an out-of-trim condition that was not identified by either pilot and resulted in control difficulty when the autopilot was disengaged.