The worst comes in the form of judgments passed on the city.  Sandburg refers to these judgments, listing them as someone speaking them out loud:  "They tell me you are wicked...crooked...brutal."  He admits that "they" are in fact correct; he doesn't deny it.  Chicago is wicked, crooked and brutal.  He describes those traits in more detail:

"painted women under the gas lamps luring the farm boys...gunman kill to go free and kill again...the marks of wanton hunger" on the "faces of women and children."

So, those traits are the worst of the city.  However, despite this, Sandburg also describes much about the city that he loves.  The best sides of it is its

"lifted head singing/so proud to be alive and coarse and strong and cunning."

He emphasizes that even in the dire, poverty-stricken misery of the city that people are "strong", "fierce", "laughing", "bragging", and happy to be alive. He emphasizes the strength of the working class of Chicago, and how they are proud to be who they are, and happy in their station, full of vivacity and life. So, Chicago is a lively, strong, intense city, and those are its best traits, mixed right in there with its worst.

What are the best and worst aspects of Chicago in the poem "Chicago"?

Sandburg paints the city with very broad strokes in his poem "Chicago." He's not interested in small, specific details; he's looking at the big picture, and he's finding it filled with activity, filled with people deeply involved in living life to its fullest.

Sandburg admits to a number of problems that are present in the city. He recognizes the presence of prostitution, of gang warfare, of poverty. He acknowledges that there is pollution and noise and greed and exploitation in the midst of all the activity and all the bustle of the city.

In spite of it all, however, Sandburg is proud of the city and is proud of his association with it. He sees the rough edges and challenges as points of pride, demonstrations of the determination to rise above the bad and accomplish the job waiting to be done.

Come and show me another city with lifted head singing
     so proud to be alive and coarse and strong and cunning.
Flinging magnetic curses amid the toil of piling job on
     job, here is a tall bold slugger set vivid against the
     little soft cities