When Bart first scores against Lisa, the scoreboard says "Pigs" rather than Home/Visitor which is correct and shown later.
When Ralph goes on stage with Principal Skinner his shirt is brown and his pants are blue. His shirt is usually blue with brown pants.
The second time Apu hits a puck at Lisa, he drops a puck on the ice beside two pucks already there, but after he strikes it there are now no pucks on the ice.
In the first hockey game when Milhouse is the goalie, Bart collects the puck at his goal line (red line). He then skates down the rink, passing his team's blue line, the center line (red) and then stops at the opposing team's blue line to shoot. When the shot changes to a wider angle the blue line has become red and there is now a blue line behind him.
The clock in Krabappel's classroom is first shown at approximately 11:27. When the scene cuts back to Ms. Krabappel, the clock reads approximately 12:23.
While Bart is taking the penalty shot, time on the scoreboard is running. In ice hockey, the clock remains stopped during a penalty shot.
In Bart's first hockey game, the scoreboard shows the team names "Pigs" and "Gougers" rather than the correct "Home" and "Visitor" that would appear on an actual scoreboard.
In the scene where Bart's ice hockey team wins and Chief Wiggum informs the team they won't be going for pizza, Homer hands Bart his turtle and in the next shot, the turtle visibly disappears from Bart's hand. In addition, Bart picks up the turtle by its shell, but it appears standing in it.
Ralph Wiggum plays for a different team than the one his father coaches.