As most hardcore Superman fans can attest, Superman, particularly in the Silver Age had numerous powers beyond his basic set of abilities. In fact, it was commonly joked Superman would gain at least one power a year he would use only once and then never again. Power such as super-eating, telekinesis, super-mathematics or projecting rainbow rays or tiny Supermen from his hands.
Most often this was because writers may have written themselves into a corner and were forced to give Superman abilities he didn't already have but could get away with creating since it was likely they would never need to utilize those powers again. Or they seemed so reasonable, no one ever questioned their existence.
Golden Age Superman
The Golden Age Superman was a titan of physical proportions. Faster than a speeding bullet, more powerful than a locomotive, able to leap 1/8 of a mile in a single bound. The most notable power he acquired was the power of flight during the late 1940s and early 1950s.
Superior Mental Acuity: He would eventually gain some mental abilities which stayed with the character over the decades. One of them was his superior intellect, total recall and his ability to learn and speak any language, almost instantly.
Silver Age Superman
- Infrequent Mind Control: During the Silver Age with tight deadlines, no worries about continuity, and the need to keep cranking out stories as fast as the artist/writer teams could manage, some superheroes like Superman would gain a power he didn't have before. In Superman #45 he uses mind control on an alien to release him from a prison.
Super-Hypnotism: One of the powers that was an on-again, off-again power, was the enigmatic: Super Hypnotism. This power enabled Superman to hypnotize anyone. He could make people forget incidents or obey his commands. This power was most often used to safeguard his secret identity.
Others were subtle such as the explanation for why Clark Kent was never mistaken for Superman. At one point, the explanation was his subtle but constant influence of his super-hypnotism (amplified by the Kryptonian glass used in his glasses - the only glass capable of surviving the use of his heat vision...) on the minds of people around him.
They perceived Clark as older, with more lines on his face, a slightly receding hairline and looking less like Superman than he normally should.
- Magical Energy Absorption: Or the ability to absorbed magical energy from the Earth to recharge himself...
Most of these overt mental powers and their related affects disappeared with the Silver Age Superman after Crisis on Infinite Earths.
However, realizing Superman's inherent vulnerability to mind powers, authors would eventually relent and give Superman back some of his mind abilities through the physical and mental martial disciplines of Torquasm Rao and Torquasm Vo.
Torquasm Vo is an ancient Kryptonian warrior discipline technique wherein he fights the opponent on a purely mental realm. These mental disciplines would help shield his mind from villains with mind control and mental domination powers.
Torquasm-Vo : known as the "theta state" and was a warrior rite of the Kryptonian race and was a psychic disciple that involved the control of ones consciousness which allowed two practitioners to battle one another. The Eradicator in its guise as Kem-L engaged in Torquasm-Vo with Kal-El in order to convert him to Kryptonian teachings.
Superman engages Dominius using Torquasm Vo.
As for examples of telekinesis...
Superman's powers have never been clearly defined. How his powers work, the actual mechanics have rarely been attempted to be explained. Eventually, handwaving would slowly enter the equation and we would be forced to accept whatever explanation of his abilities.
During the Post-Crisis era, the writer, John Byrne tried to postulate Superman's abilities were, at least in part, psychically derived. His ability to lift objects without crumbling under their own weight was considered to be, in effect a telekinetic aura which protected anything he lifted, such as an ocean liner or aircraft. He's been shown to throw objects such as the Daily Planet's globe which should crumble when the energy of his hands were placed on particular points beneath it.
- Superman used a cargo ship like a battering ram against the powerful government alien agent of The Machine, Wraith in Superman Unchained #8. The ship remains in one piece as he flies it into the Gobi desert...
- This power of "tactile telekinesis" was used as the basis of the powers of the cloned Post-Crisis Superboy.