* What kind of football? Are you talking about American football, soccer, or another type of football?
* What level of play? Are we talking about professional, college, high school, or amateur games?
* Highest score by one team or combined score? Are you interested in the highest score a single team has achieved, or the highest combined score of both teams in a single game?
For example, in American football, the highest score ever recorded in a professional game was 72 points, achieved by the Chicago Bears against the Washington Redskins in 1940. However, the highest combined score in a professional game was 104 points in a game between the New York Giants and the Philadelphia Eagles in 1961.
In soccer, the highest score in a professional game was a 149-0 victory by AS Adema over SO l'Emyrne in 2002. This result, however, is considered highly controversial and is thought to be a result of a deliberate act of protest.
To get a more accurate answer, you'll need to specify which kind of football and level of play you're interested in.