Near the end of the big game, Marko is standing within a circle of the other hockey players; in an overhead shot we see him lean down to grab his gloves and put them back on - his discarded stick is nowhere in sight. But in the next overhead shot, Eliot skates up to the stick which is right next to Marko and hands it to him.
After Marko picks up his gloves and Elliot hands him his stick and says "lets go play some hockey" the play starts without a face off.
When the stoppage of play in the big game comes to an end, Eliot skates onto the rink from either the penalty box or team bench, hands Marko his stick, and says "let's play some hockey." Eliot then skates off to start play - but if he was in the penalty box, he would have to have finished his penalty time before rejoining play, and if he was on the team bench, then he would represent an extra player on the ice, which is against the rules.
After the winning goal is scored in the last game with about 3.7 seconds left, the clock continues to run and the horn sounds ending the game. The clock should have stopped when the puck crossed the goal line, and there should have been time left (albeit very little) for a face-off.
At about 36:40, when Eliot says, "Let's play some hockey", the fans in the stadium seats behind them are a still image of a crowd. Noticeable because many are looking slightly off to the left, away from the central action, and no one is moving.