(at around 30 mins) When the Mole Men are chased and trapped on top of the dam, it is nighttime. After they get away from the dam, they are being chased again and it is clearly daytime.
(at around 51 mins) When Clark runs into the alley, the same one that is in Metropolis, there are two 55 gallon drums at the entrance. The second time, there is only one.
At around 6 minutes into the film, a man states that the oil drill dug 5 miles down. Lois Lane then says that is nearly to the center of the Earth. In fact, you would have to drill nearly 4,000 miles to reach the true center of the earth. However, "the center of the earth" is a common convenient expression to mean "unbelievably far down," as in the often-filmed Jules Verne novel Journey to the Center of the Earth (where the explorers only ever go about 5 miles down) rather than a literal measurement. It is a figure of speech, like "the sun rises in the East" or "this is the middle of the ocean" - it's useful for describing what is shown, but is not scientifically accurate.
(at around 12 mins) When Lois Lane describes the mole men after her first encounter with them, she describes them as having human heads with the body of moles. The only costume the actors playing the mole men wear is a dark, presumably furry suit that conforms to their human shape. A few times during the film the zipper in the back of their costumes can be clearly seen.
Obvious bald caps on the Mole Men.
(at around 28 mins) When the Mole Men are atop the dam, they are in a small rectangular area of the screen in a different shade of black than the night sky around them, revealing that they were just "superimposed" into the shot.
When the mole man is escaping the mob crawling over the rocks you can see the zipper in the back of his costume.
(at around 30 mins) Two Mole Men are shot at and one of them goes down right away but the other hesitates before slowly going down, as if the actor was waiting for the sound of a second shot.
(at around 47 mins) When Clark tells Lois that he sees Craig and Corrigan running up the street, she doesn't see them until they turn a corner, so he must have been using his X-Ray vision, a sure tip-off he's Superman.