It's true that the seats by the exits on the older 737s don't have any trays. They row forward of the exit is situated so that it faces the rear. That way they can squeeze in an extra row of seats, each with only half the foot room of normal rows. Don't sit there if you can help it. Because they don't have any seats where the trays come out of the arms, those rows also do not have any trays. I've never seen a pillow on a SW plane either.