Revealing mistake: Superman has just saved Jimmy at the dam and is holding him in the air. Jimmy's fringe is standing up thanks to some hair fixer to achieve the effect of wind blowing (though it's a green screen effect). When Superman sets him on the floor his hair remains up giving away the trick, until the angle changes and it looks all combed and nice.
Sacha
Continuity mistake: When Clark shows Perry a white paper with directions of where to send the payroll, the way he holds the paper differs between shots.
Sacha Continuity mistake: The first wide shot of Superman arriving at the broken railway shows no logs hanging. The close shots, and then on, do show logs.
Sacha Continuity mistake: When Lois exits the alley where Clark grabs the bullet, her hair is much shorter than when she entered.
Sacha Continuity mistake: When Superman arrives at the ditch by the railway, the gap is 3 times his length. In the next shot the gap has shrunk and now measures exactly Superman's height.
Sacha Continuity mistake: When Superman is in Luthor's lair and Lex calls Ms. Teschmaker , the lamp on the floor changes from lit to unlit depending on the shot.
Sacha Revealing mistake: When Superman takes Otis and Luthor to the prison wires holding them are visible.
Sacha Continuity mistake: When Superman walks to Luthor's lair, the amount of snow on the bridge of the snow-chamber differs between the CCTV shot and the one from the inside.
Sacha Revealing mistake: When Superman leaves the prison, wires holding him are visible.
Sacha Continuity mistake: After Superman breaks Luthor's door, on Lex's table a map is resting on a sculpture on the left. From a back shot, it isn't.
Sacha Revealing mistake: When Superman lands the burglar, wires holding him are visible for a brief moment.
Sacha 
Revealing mistake: Under Grand Central, the train that passes by Otis is the same one (5048) that kills the cop.
Sacha Revealing mistake: In Grand Central Station, the same extras appear in every scene, no matter where in time or place occurs.
Sacha Continuity mistake: When Clark is shot by the mugger, his hat falls down. In the next shot, while Lois is screaming, you can see him taking his hat off.
Sacha Revealing mistake: After Superman saves the cat, he takes off and wires holding him are visible.
Sacha Continuity mistake: When the council tells Jor-El not to worry them, a bald man standing in the back changes positions between shots.
Sacha Continuity mistake: The position of the baby when his mother holds him by the cradle differs in the wide and close shots.
Sacha Continuity mistake: After Clark runs by the train, a girl in a moving car stands up. In the next angle, a split second later, she is sitting down.
Sacha Other mistake: Clark does not have enough room beneath his clothes to have the suit, the cape and the boots.
oswal13
Revealing mistake: Before the Hoover Dam breaks, the places where all the cracks and water will later appear are easily traced on the concrete, covered in plaster and painted. Either that, or the real Hoover Dam has burst many many times and always through the same spots.
Sacha 
Answer: Superman has chosen to use his powers on Earth for the good of mankind. It would seem that lying to them would be an unneccessary thing to do, so it appears to be a personal choice. Interesting trivia: the closest he comes to lying is when he tells Lex Luthor to get Zod and company into the molecule chamber in the second film. Listen closely, he only says that it is a molecule chamber that takes away their powers, he never actually says that being inside will make them lose them, only that he wants Luthor to get them to go into it.
JazetopherThat may be the closest "Superman" comes to lying, but Clark Kent does appear to lie. After the mugging scene in the first movie, Clark tells Lois the contents of her purse, and when asked how he knew (obviously from his X-ray vision), he says "wild guess" which was a lie.
jimbaNot only that but, he spent his whole life pretending to be ordinary so, in fact, he spent his whole life living a lie.