When the marshal crashes his car, the airbags deploy and smoke comes out of the front of the car. When Kate kicks him out of the car, she is able to start the car and drive away, the front of the car is completely intact save for a slightly crooked and dirty front license plate, and the airbags are nowhere to be seen.
Kate's father's desk nameplate reads the rank of sergeant, but his rank according to his uniform is sergeant major.
When Kate is riding in the car with the marshal, they crash and the airbag deploys and knocks out the marshal. Shortly thereafter, she drives the car away. In most cars, after the airbag deploys, the whole steering column needs to be replaced and the car wouldn't be able to drive at all.
(at around 41 mins) When Kate and Sawyer see the horse, there are several frames of what appears to be a trainer's hand, getting the horse's attention with a black glove on. Possibly only visible in widescreen.
When Mr. Eko tells Locke the story about King Josiah and the Book of Law, he refers to the Book of Law, saying: "You may know it as the Old Testament." The Book of Law is the Torah, which actually comprises only the first five books of the Old Testament, Genesis through Deuteronomy.