This 3 band radio has 3 antenna screws, one is unmarked, the others are A and A. When I connect a long wire to the unmarked (left) connection, I get great am reception, but poor shortwave. What are the others for? Are they for a short wave only antenna?

Should be marked "A", "Z", and "G" in that order from left to right. "G" = ground (physically connected to the chassis). "A"= longwire antenna. The "Z" connection is used with the "A" port for a doublet antenna; if a doublet is not used the "Z" and "G" ports are usually tied together with a shorting bar (may vary from model to model).

You should get good reception on both BC and SW with a longwave antenna connected to "A". If SW reception is poor you may need to align the front end for that band setting.