When Clark leaves his office to get the dog from the dogcatcher, he doesn't have a hat, when he gets to the storeroom to change into Superman, he is wearing one.
When Superman rescues the dog from drowning in the well, Superman is wet, but the dog is dry. (This may be because the first thing a wet dog does is shake water on everyone around.)
The crooks apartment front door opens outward when generally they open inward. This is done as a security feature so nobody can get to the door hinges from the outside.
When Jimmy picks the dog up off Clark's desk a paper is brushed off and falls to the floor. Both Lois and Clark see this happen yet do not bother to pick it up.
When Lois has Jimmy drive her to the crooks apartment to return the dog and maybe get a story neither of them know how long it will take her yet when she returns to the car where Jimmy is waiting for her the car door is already opened and apparently has been left that way.
One is unsure of Corky's gender as the pup is referred to as both a girl and a boy at different times.
When the dog runs out the apartment door, no one thinks to look for the dog in the hallway. The building door would normally have been closed and the dog would still have been in the building a minute after leaving the apartment.
While Louie is in Clark's office, the shadow of the boom microphone is visible several times moving around in the upper left side of the screen.