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.
Other mistake: Just before the Charger crashes, a tow bar connecting both vehicles is visible on the Mustang's front bumper.
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.
Answer: The man shot at the hotel at the beginning is Renick. Ross assumed Renick's identity and was going to flee the country. Ross kills Mrs. Renick to keep her quiet. The man at the airport that Bullitt kills is Ross.