B. The molecule contains phenolic hydroxyl, which can react with FeCl3 solution, so B is wrong;

C. If there are two benzene rings and one C=C that can react with hydrogen, then 1mol of rosmarinic acid will react with H2, which consumes at most 7 mol of H2, so C is wrong;

D. The molecule contains four phenolic hydroxyl groups, one carboxyl group and one ester group (which is hydrolyzed to produce alcohol and carboxyl group), then 1mol of rosmarinic acid reacts with enough NaOH solution, and at most 6 mol of NaOH is consumed, so D is correct.

Therefore, D is selected.