Continuity mistake: During the chase, when Bill Hickman drives the Charger into the residential area, as he loses Bullitt he comes to a distinctive intersection: he first looks right, then left. As he looks left, the first view of the sky shows it is half full of light clouds. A moment later, when the car drives on, the sky is completely clear of clouds. There are other shots showing even heavy clouds/blue sky, too.
Continuity mistake: In the leadup to the chase, the Charger stops at the top of a hill and the occupants look left where we see a green car parked in front of a red car. As the Charger pulls away we get the same view. The red car is still there, but now has a blue car of a different model in front of it and in a different place.