By happy coincidence, TCM had "Ben Hur" on tonight. I think that was a camera car that had been taking closeups, and was then pulling out of the way. It was caught by the camera up in the stadium, and they probably decided to leave it in, hoping nobody would notice. In that same scene, the five parade horses were missing, but they reappeared in the next scene.
I don't know how many days it took to shoot all the scenes, but it must have been a costly project. Some of the action was speeded up, but just getting all those horses and drivers on the set for the parade lap was quite an acomplishment.