At the start of the Chinese Downhill, everyone is wearing the same outfits that have been worn throughout the entire movie. For some reason Harkin's distinctive (if not signature) blue and black stretch pants have changed to black with red piping. It seems unlikely that the farm boy would buy new ones just for the downhill. Let alone ones that are the same color scheme as his nemesis.
Harkin's bindings and skis change during the opening downhill scene. His mostly white Look bindings change to red. And his white Dynastar skis switch to black or dark blue Rossignols. This is most evident when he skis "over" the camera, in a tuck, near the end of the scene.
When Squirrel gets into the 4 person gondola with the pretty girl he hands his skis to the attendant who puts them in the front ski basket... In the next scene of the gondola coming out there are no skis in the basket.
During multiple shots, especially during the "Chinese Downhill" preparation sequence, the cameras and film crew are visible in the reflections off the actors' helmets. (e.q. "Squirrel Murphy" and "Rudette.")
When Dan challenges Rudy to the Chinese Downhill, he states, "Forty bucks a man, winner takes all." At the start of the race, the announcer says that the winner will get $2300. 2300 doesn't divide evenly by 40. Further, only about 26 racers can be seen at the start. That would make the grand total $1040.
The plot includes the awarding of a gold medal at Lake Placid to a freestyle skier. The Winter Olympics at Lake Placid took place in 1980. Freestyle skiing wasn't even an Olympic demonstration event until the 1988 Winter Olympics in Calgary. Mogul skiing was added as an official medal event at the 1992 Winter Olympics in Albertville, and the aerials event was added for the 1994 Winter Olympics in Lillehammer.