At some races the start and finish lines are at different places, Imola is one and I think the A1 ring and Assen. Wasn't some one on here just at Assen? They can correct me on that.
Usually it's a case of the start line being near the middle-end of the straight and the finish line being much nearer the beginning of it. It allows for a full grid to line up on the straight while using the safest/convenient finish line.
I can't think of any tracks where they are on different straights but every Supercross race ever run uses separate start and finish lines, as do most motocross tracks.
I'm not saying it's the best solution but, in racing, it's not unheard of.