On June 19, 2005, at 1430 eastern daylight time, a Piper PA-28R-200, N4313X, registered to Tango Sierra Holding Company, leased to Falcon Flight Center, operating as a 14 CFR Part 91 instructional flight, received substantial damage to the left wing on landing at Daytona Beach International Airport. Visual meteorological conditions prevailed and no flight plan was filed. The damage was observed and reported to the NTSB on June 22, 2005. The commercial pilot flight instructor (CFI) and private pilot receiving instruction reported no injuries. The flight originated from Daytona Beach International Airport, Daytona Beach, Florida, on June 19, 2005, at 1300. The CFI stated the private pilot receiving instruction was conducting take offs and landings with a crosswind estimated between 10 to 11 knots to runway 7 right at Daytona Beach International Airport. On one approach the private pilot put in a left crosswind correction for the crosswind. The pilot did not take out the crosswind correction before touch down and the airplane landed abruptly with a side load on the left main landing gear. The CFI stated he was late in taking corrective action to prevent the side load. After the airplane touched down the gear in transit light would not go off during gear retraction. The CFI stated he did not observed any damage to the airplane after the flight was completed, and he did not write up the gear in transit light on the maintenance discrepancy log. The CFI stated he did mention the discrepancy to the airplane dispatcher. The private pilot confirmed the statements made by the CFI and stated she did not conduct a post flight inspection of the airplane after the flight. The owner of Falcon Flight Center stated he flew an instructional flight on June 20, 2005 ion N4313X, and they conducted short field take offs and landings. The landing gear transit light illuminated on initial climb out. The landing gear was recycled, and they continued with the flight. Upon completion of the flight the airplane was taxied to maintenance hangar and no post flight inspection was conducted. The Director of Maintenance for Falcon Flight Center stated he looked at the nose gear limit switch. The up side of the limit switch had slipped out of position. The limit switch was moved back into position and tightened. He further stated he did not examine the limit switches on the main landing gear, and he did not notice any damage to the airplane. He asked a lineman to move the airplane back to the ramp. On June 22, 2005, he was notified by an airplane refueler that N4313X had damage to the left wing. Examination of the airplane on June 28, 2005, revealed a 3-inch tear on the top of the left wing skin adjacent to the fuel cap. Further examination revealed half of the rivets had pulled out of the wing skin and the rib located next to the left main landing gear strut. The left main landing gear transition micro switch was displaced and the landing gear transit light remained in the on position. A functional landing gear retraction test was completed and no anomalies were noted except for the landing gear transit light remained illuminated. Falcon Flight Center Safety Procedures and Practices sates in Aircraft Discrepancies, " All Falcon aircraft discrepancies must be entered in the Maintenance Discrepancy Log."