Other mistake: Whenever Fozzie is driving the Studebaker, the movements of the car don't correspond to the way he moves the steering wheel (he tends to crank it back and forth a lot).
Other mistake: In the fight scene right after Miss Piggy blasts the man through the wall, she kicks another man. If you look closely, he goes back from the kick a little, then just stands there and adjusts his hat.
Other mistake: As Fozzie corrects the car to keep from crashing, watch the two of them in the long shot by the church. They are bouncing very rapidly as they come to a stop, suggesting the film was sped up. Also, Fozzie looks to the left of the steering wheel to shift gears, rather than the right, where the shifter would be, on the transmission hump.
Other mistake: When Fozzie backs his car into Hopper's and then leaves, the front of the Caddy shows no damage, despite the severity of the hit. Not even a speck of paint on the bumper.
Answer: Fozzie did not mean to sing the National Anthem. He simply wanted to sing something patriotic, since he was so moved by the scenery.
Matty Blast