This is a great question. Notice how the story of the dog begins with very short pieces of dialogue and little information. The dialogue is casual. Scout says, "Whatcha looking at?" (92) as though nothing very important is happening, and Jem's reply does not indicate any kind of concern. But as the scene goes on, the reader can see that whatever is wrong with the dog is more serious than a cut on the dog's paw. Once Calipurnia sees the dog, Scout relates to us that Calipurnia starts making phone calls, shouting into the phone. We can feel her panic.
Once Atticus arrives, things get quieter. The street is silent, and the dog is moving slowly. This quietness actually increases the tension, just as a scene in a movie might get very quiet right before the killer strikes.
The tension increases as Heck Tate and Atticus talk about who will shoot the dog because once the dog turns the corner, there could be any number of people the dog could attack, and time grows short as they argue. Finally, Atticus shoots the dog, which at this point is heading down his street, placing his own children at risk. There is a kind of letdown in the scene because Atticus shoots with sadness, so there is no triumphant ending. There are really no "bad guys," just an old, sad dog with rabies.
The use of the rising action, then the "quiet before the storm," and then the final shot make the scene very tense, don't you think?
Of course, as a follow up to this scene, the children learn something they did not know about their father's shooting skills. But that is another story!