Bill, are you sure about printing? This 2nd ed is stated as "Third printing" on the first page but actually, it seems that all 2nd and 3rd ed have the same "Third printing" stated on the first page.
My
2E "Third printing" has X instead of D&D.
My 1st
3E "Third printing" has D&D and no X.
My 2nd
3E "Third printing" has X instead of D&D.
No other difference between the two
3E "Third printing".
I remember a discussion with David/faro about that but I can remember our conclusion. A clear difference could be the ink color on cover though (black, brown, or blue).