Continuity mistake: During the game against the Soviet Union, the US team ties up the score at 3-3. As Al Michaels comments on the tied score the crowd is panned and the scoreboard reads 4-3, which actually happens a few minutes later in the game. The digits are hard to read, but if you look closely enough, the mistake is detectable.
Continuity mistake: During the series of sprints that the coach makes the players do after the game against Norway, the number of players on the ice changes. This is especially evident during the first one they do in the dark (only about 16 or 17 skaters are shown instead of the original 21).
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Continuity mistake: After the coach's first argument with his wife, he returns to the bedroom to apologize. She's laying on her right hip and has to twist at the waist to see him standing in the doorway. He speaks, and the top of her head is in the shot the entire time. When the camera cuts back to her, she's now laying on her left hip, facing him square on. She couldn't have rolled over without causing her head to move or dip out of frame.
Continuity mistake: After Team USA beat Czechoslovakia, there's a scene on the streets of Lake Placid where Herb Brooks and his advisor are discussing why there is so much media covering the hockey team. Brooks makes the statement, "They've (USA) won two games." Actually at that point, they had won only one game, against the Czechs. They tied their first game vs. Sweden.