When Dale plays home movies of Hank in high school, he says that Hank was a senior in 1979. In a flashback in another episode, Hank was a senior in 1974.
The length of Dale's cigarette that Bobby uses to re-ignite the torch changes between shots.
When Hank falls and the torch goes out, he has to relight it from a cigarette Dale lit from the torch. In fact, the torch relay organizers always have at least one miner's lamp that was lit from the flame in Athens for just such an emergency.
Peggy tells Bobby not to get close to the plants on Bobby's "trophy" shelf because they will suck the oxygen right out of him. Plants don't take in oxygen; they take in carbon dioxide and produce oxygen.
The Olympic rings on Hank's sweats are upside-down.
Dale's shirt at the torch running says "TOWEL MANAGER" on it. In one frame, right before Hank extinguishes the torch, the "M" is missing, so it says "TOWEL ANAGER."
Spiking the ball and excessive celebrations after touchdowns are not allowed in high school football. It is a 15-yard unsportsmanlike conduct penalty.