The Silver Age Superman is, to my mind, the greatest of all superheroes, but I must admit that he doesn't always employ the wisest strategy in the Never-ending Battle for Truth, Justice and the American Way. Specifically, he is far from the best secret-keeper in the world.
Any military or police strategist would agree that it's best to keep the bad guys in the dark about your capabilities, as far as possible. Superman himself clearly accepts this premise when he decides to keep the existence of Supergirl hidden for years after her arrival on Earth, in part so that she can be his "secret weapon" against crime.
On his own behalf, though, he sometimes drops the ball. For example, he would be wise to keep the extent of both his powers and his weaknesses as secret as possible, to avoid giving away any advantages to either super-criminals like Lex Luthor and Brainiac or common criminals like bank robbers and racketeers. Clearly, some of his powers are too obvious to hide, like flying, super-strength and super-speed, but why let people know he has super-hearing? It's much easier to overhear evil plotting if the plotters have no reason to believe you can hear them. Similarly, why let people know he has x-ray vision, or heat vision, or any of his other "stealth" powers?
Even assuming that Superman is so confident in his powers that he doesn't care if his foes know about them, we must wonder why he goes to the extreme of revealing his weaknesses, both physical and psychological. Superman's vulnerability to the various types of kryptonite is so-well known as to be the subject of Sunday Supplements in the Daily Planet. It seems that no criminal, whether mastermind or petty thief, sets up shop in Metropolis or its suburbs without first procuring at least one piece of kryptonite. A wiser man than Our Hero would never let anyone know kryptonite exists, much less reveal its effect on him.
Superman even reveals his smaller weaknesses. Knowing that neither his x-ray vision nor his heat vision can penetrate lead, Lex Luthor and others have lined their hideouts with thin sheets of lead. One assumes they regard the poisonous nature of lead to be a worthwhile price to pay for some measure of protection against their arch-enemy.
Perhaps the most stunning example of poor secret-keeping is the fact that it is fairly common knowledge that Superman has a secret identity---someone he is, when he's not being Superman. Consider that Superman, unlike most of his fellow superheroes, wears no mask. This would suggest to the public that he is not hiding who he is, because he's always Superman. People would not assume he has any identity other than Superman, but, somehow, he has let that secret out. Keeping the secret of his dual identity is psychologically important because Clark Kent provides him a way of interacting with ordinary humans as peers, as well as giving him some measure of privacy, away from constant demands on Superman. Thus, the fact that people know he has a secret identity, even though very few know who that secret identity is, needlessly lessens its usefulness.
Superman, you know I love you like a brother, but maybe you should talk strategy with the Batman.