The front door of Dr. Jessup's house is dark in color. But when Clark and Lois are inside, both the inside and outside faces of the front door are an almost off-white color.
There is never an explanation as to where Clark Kent keeps his clothes when he becomes Superman and vice versa.
At around the 24 minute mark while digging, Lois finds the Drill Core in the cave. Clark takes them from her. As the two exit the cave in the next scene, the Drill Core disappears from Clarks hand. Moments later when they exit the cave, the Drill Core reappear in Clarks hands.