Woody initially doesn't want to enter the basketball pool because he says he doesn't like taking money from his friends. Then when he wins he is a poor sport by gloating, implying that he has never won a betting pool and doesn't know how to behave properly. However, in season 4, in Fools and Their Money (1985), the main story line revolves around Woody having been active in the Cheers football pool, and having won three weeks in a row - without gloating.
When Carla receives the flowers, with a card from "your loving husband, Edward LeBec," she knows that they are not from Eddie because his real first name is not Edward, it's Guy (pronounced "Ghee" in French). However, in Little Carla, Happy at Last: Part 2 (1987) the priest at their wedding referred to him as "Edward" and as "Edward Raymond".
Carla makes a call using a second payphone located beside the scoreboard of the pool room wall that is not normally there.
Highly unlikely that a small bar could have a betting pool on just a regular season game, since you have to sell 100 squares in just a few days with limited interest in the game. That's why Super Bowl pools are popular -- there's more game hype and there's weeks to fill the squares.
Camera position spike tape visible in wide shots of the bar form the TV point of view.