Moments before the bomb goes off in President Bateo's office, Superman breaks through the wall and is covered in white dust. Further, he jumps on top of the bomb and when it goes off he is covered with more debris. A moment later he is completely clean.
Mr White and Lois are ringing the doorbell as Superman returns to his hotel room, through the window. He walks off-camera and after one doorbell ring, reappears; he's now wearing his glasses and a bathrobe. The latter hides what he's wearing from the knee up. There wasn't time to remove his Superman costume and get re-dressed, but as he lies down on the bed, instead of the blue tights and red boots expected, he's wearing gray pants, black socks and black shoes.
Superman uses his power to split himself into two equal entities. This is the first and last he has done this. Why would he not do this at least one time to prove he and Clark Kent could be in the same place and the same time to prove they were two different people.
Superman splits into 2, so that one of him can remain in the cell, but the other can be free to do what is needed. But the 2nd Superman basically did nothing. He flew to his hotel, took a nap, the flew out to the mine. The other Superman left the cell, and also flew to the mine. Then the Supermen merged back into one.