Juvenal's Satire III
The first most challenging social problem in the United States is the unemployment.
"Codrus possessed a bed too small for the dwarf Procula, a sideboard adorned by six pipkins, with a small drinking cup, and a recumbent Chiron below, and an old chest containing Greek books whose divine lays were being gnawed by unlettered mice. Poor Codrus had nothing, it is true: but he lost that nothing, which was his all; and the last straw in his heap of misery is this, that though he is destitute and begging for a bite, no one will help him with a meal, no one offer him lodging or shelter." The effect of an unemployment seen in one's living conditions. Although this is not the only evidence of poverty, because the kind of poverty we deal with in America is a little different. Most people suffer from poverty because of unemployment therefore struggling with food and living conditions. 

The second social problem that we see across the United States is obesity.
"yes, at a single meal from their many fine large and antique tables they devour whole fortunes. Ere long no parasites will be left! Who can bear to see luxury so mean? What a huge gullet to have a whole boar—an animal created for conviviality—served up to it! But you will soon pay for it, my friend, when you take off your clothes, and with distended stomach carry your peacock into the bath undigested! " (satire II)Obesity is caused due to bad lifestyle and diet. In this quote it compares the wealthy to parasites - who consume anything. Their stomachs are described as having peacocks in them. Obesity in a sense was not so much of a health problem as much as it was a sign of over-indulgence, greed, corruption - everything juvenal would associate with the wealthy.

The third social problem is the recent discussion over legalizing same sex marriage.
"By degrees you will be welcomed by those who in their homes put long fillets round their brows, swathe themselves with necklaces, and propitiate the Bona Dea with the stomach of a porker and a huge bowl of wine, though by an evil usage the Goddess warns off all women from entering the door; none but males may approach her altar.[15] "Away with you! profane women" is the cry; "no booming horn, no she-minstrels here!" Such were the secret torchlight orgies with which the Baptae[16] wearied the Cecropian[17] Cotytto. One prolongs his eyebrows with some damp soot staining the edge of a needle, and lifts up his blinking eyes to be painted; another drinks out of an obscenely-shaped glass, and ties up his long locks in a gilded net; he is clothed in blue checks, or smooth-faced green; the attendant swears by Juno like his master. Another holds in his hand a mirror like that carried by the effeminate Otho: a trophy of the Auruncan Actor,[18] in which he gazed at his own image in full armour when he was just ready to give the order to advance--a thing notable and novel in the annals of our time, a mirror among the kit of Civil War! It needed, in truth, a mighty general to slay Galba, and keep his own skin"
Men are now dressing and acting more "feminine", which is a sign of gender inversion. Same sex relationships and marriages do stem from the controversy over the what roles of woman and men are and the traditional structure of a family. Likewise, in rome, the gender roles are being challenged in the way they dress.

The fourth social problem is global warming and environmental changesThe works of Juvenal don't talk about the dangers of global warming or environmental effects on the economy of Rome. I doubt that was of major concern during that time. The negative environmental consequences of disasters and bad weather may be seen as signs of the god's disapproval or curses. Weather patterns were very much controlled by the gods, like Juno who enlists the help of Aeolus, who sent mighty winds in hopes to destroy aeneas' ship in the first book of the aeneid. In satire II they do have a quote which does reveal that the wrath of heaven will cause us to weep and the gods could bring upon the people curses if they feel inclined to do so.
"he exiled Marius[15] carouses from the eighth hour of the day and revels in the wrath of Heaven, while you, poor Province, win your cause and weep!"

The fifth social problem is poverty.
 "It is no easy matter, anywhere, for a man to rise when poverty stands in the way of his merits: but nowhere is the effort harder than in Rome, where you must pay a big rent for a wretched lodging, a big sum to fill the bellies of your slaves, and buy a frugal dinner for yourself. ""Who but the wealthy get sleep in Rome? There lies the root of the disorder. "Poverty was definitely a big issue back in rome. That is one of the clear reasons why juvenal left rome in the first place. The social gap was very evident and a huge issue.