Question: At various points in the film the car brakes are glowing red hot, would this happen in real life or is it for show?
Answer: I watched this movie with my father, who actually participated in Autocross races in the past. He says from first hand experience that this is indeed real. The breaks get so heated from use in the race during the rapid slowing and going that they glow hot. This is why there are racing grade breaks and it's unwise to try and race without them.
Agreed. My dad is a former race car mechanic and he said that this absolutely happens all the time.
Answer: Watch any NASCAR short track night race where heavy braking is required, the brake rotors glow at every turn.