When the pilot selected the landing gear up after takeoff, the gear unsafe light remained on. Recycling the gear had no effect. The pilot continued to his planned destination, with the aircraft performing at about 10 knots below the expected speed. On arrival, a visual inspection confirmed that the right maingear was trailing. The pilot then carried out a successful emergency landing, during which the right flap and propeller sustained damage as the gear collapsed. Subsequent investigation disclosed that the right gear strut had failed on takeoff from Mudgee. Examination of the failure indicated that corrosion fatigue had initiated on the inner surface of the strut. The strut had not been subjected to corrosion prevention methods. An inspection cycle recommended by the manufacturer had not been followed.