After Kelly Leak's homerun gives the Bears their first win of the season (against the White Sox) the footage of the Bears celebrating at home plate around Kelly shows a Yankee catcher. This footage was actually from the alternate ending which had the Bears winning the final game against the Yankees.
When the Bears are playing the Yankees in the championship game, you can hear the announcer state that the bears are leading 1-0. However, a later shot of the scoreboard shows that the Yankees were actually the first team to score.
When Rudi Stein is first asked by Buttermaker to let himself get hit by a pitch, he is following Kelly Leak in the batting order (Kelly had just been walked intentionally). When he's asked the second time, he's following Ahmad in the batting order.
On picture day, Buttermaker has his arms crossed trying to hide his beer. He then has his arms uncrossed as the photographer snaps the picture. When the camera cuts back, he is again standing in the original pose, with arms crossed trying to hide the beer.
After Tanner has a fight with a Yankee Player at the snack bar, he is placed in a garbage can by the Yankee Player. Lupus picks up Tanner's hat and places it in Tanner's lap right side up. The next shot shows the hat in his lap upside down.
When the Bears play the Athletics the game before the championship game, the scoreboard says the home team is winning 1-0 the first time we see it. The second time we see it, the visitors are winning 1-0. The third time we see it, the home team is winning 2-1.
In the dugout, during the final game against the Yankees, Coach Buttermaker's beer switches from a 16-ounce can of Coors, to a brown glass bottle of Lucky Lager, and back again to Coors, all within a matter of seconds.
Several times during the course of the movie, the league standings are displayed, but the numbers shown are mathematically impossible. The total number of wins and losses for all teams in a baseball league must be even (since there is a winner and loser of each game). But every time the standings are shown in this film, those numbers don't match. In one scene, the standings show every team with a .500 record or better, which cannot happen mathematically.
In the championship game the Yankees' pitcher was allowed to remain in the game despite the manager making his second trip to the mound in an inning. The first trip was to discuss strategy and the second trip was to strike the pitcher after he threw at a Bears' batter.
After losing an air hockey match to Kelly, Amanda must go to a Rolling Stones concert with him. The movie takes place in 1976 yet The Rolling Stones did not play in or around the Los Angeles area until 1978. And that was at Anaheim Stadium. Their previous L.A. appearance was in July, 1975.