The buckling sidewalk suggests the crumbling of the social community of the town. The grass growing in the "seams" of the sidewalk resembles the look of an abandoned cemetery. 

Mr. Leonard Mead enjoys his walks at night despite the fact that his journey around town is described as follows:

Not unequal to walking through a graveyard where only the faintest glimmers of firefly light appeared in flickers behind the windows.

Nevertheless, Mr. Mead finds his nightly excursions a small respite from the loneliness of his own home. Outdoors, at least, he can get a glimpse of "the gray phantoms where a curtain has not been drawn" and imagine for a few moments that he still has some human contact. Sometimes a window has been left open and, to his delight, Mr. Mead can hear human voices. As he walks along, Mr. Mead whispers to the occupants inside the houses because this is an opportunity for him to talk to someone. He asks these huddled shadows what they are watching on the television. Unfortunately, he receives no response because the "shadows" enclosed in their houses watch the television screens with the fascination that man watched fire when it was first discovered. Cloistered in this manner, the residents are unaware of the crumbling sidewalk outside, the presence of one lonely man, and the death of a community.

The buckling sidewalk Bradbury describes in “The Pedestrian” shows a couple of things about the society.  First of all, the sidewalks aren’t being used by the people in this city.  People have locked themselves away in their homes to watch television and are not using the sidewalks or going outdoors like Leonard Mead does on his nightly strolls alone.  The sidewalks also symbolize that this society is metaphorically crumbling.  The infrastructure of the city is in disrepair and falling apart much like the people who have turned their lives over to the entertainment television provides.  They no longer need the books and magazines Mead once wrote for, and they have sequestered themselves away in their dark, empty homes to escape.  The city of nearly three million where this story takes place has become a ghost town full of shadow “phantoms” watching television in their homes.

The crumbling sidewalks show that this society is in disarray and falling apart.  Because the people don’t go outdoors and enjoy walking, they have let the sidewalks break apart without demanding they be repaired.  All they care about is entertaining themselves and are not concerned about what is crumbling around them.