Certainly racism is the largest social issue in this play. It appears in a variety of ways. First, consider the jobs that the characters hold; Walter Lee is a chauffeur, and Mama and Ruth are domestic workers. For poor African-Americans, who lacked education, these were the only options - working in subservient positions. Beneatha is trying to avoid that, by attending college and aspiring to be a doctor. Second, consider the location that Mama chose for the home she purchased. When asked why she didn't buy in the black neighborhoods, she replied that those homes cost more money and are poorly made/maintained. This is akin to redlining - a practice that lenders used to discriminate against African-Americans looking to borrow money to buy homes in which they charge higher interest rates to black borrowers. And, last, there is the visit from Mr. Lindner, representing the Clybourne Park neighborhood. Even though he is polite and respectful in tone, his message is very clear. They do not want the Younger family in their midst.
Another social issue you might want to include are those of gender roles. Even Walter is skeptical of Beneatha's aspiration to be a doctor. At one point he wonders why she can't just be a nurse. The play features very strong women - Mama, Ruth, Beneatha - but they rely on Walter to be the man of the family and make decisions for all of them.
The play was first presented in 1959 and forecasts many of the problems and issues that would divide American society in the 1960's. The first issue the play deals with is a lack of economic opportunity for Black families. All the characters accept Beneatha are working at rather menial jobs. What is unusual is that Beneatha wants a college education in order to become a doctor, but even her own brother questions that when he says "Why don't you just be a nurse, like everyone else?" Another issue that is key to the play is integration. The neighbors of Clybourne Park are obviously predecessors ofthe opponents of integration that made that issue so divisive in the 1960's. Finally, there is an inkling of the "Black is Beautiful" movement that began in the last 1960's and continued into the 1970's. Beneatha is very interested in her cultural heritage and going "natural". All of these issues affect the Younger family who are obviously a symbol for Black Americans.
Everyone has listed the most significant social issues of the play; the one I'd like to add is not as prevalent in the story, but it's important nonetheless. Ruth has discovered she's pregnant and it's not the happy news it is for most expectant mothers. She understands this means one more mouth to feed, one more sleeping space to find, and one more child to worry about growing up in this rather depressing environment. She visits a female "doctor," and she has put a deposit down on an abortion procedure. This was a social taboo, of course; but more importantly, this went against her own cultural, family, and personal beliefs. This was obviously not an easy decision for Ruth, but she felt trapped in a way few of us understand. We're thankful right along with them when the Youngers are able to find some hope--which means Ruth can do what she wants to do rather than what she felt she must do.
#4 is right in identifying some of the main social issues that are referred to implicitly or explicitly in the play. Certainly in my mind the two issues that stand out most are that of gender roles. Bennie in the play is a woman who is not content with merely fulfilling the role that society would have her play. She would be happy to marry a man like George Murchison if she were and certainly would not be trying to achieve the post of doctor in such a white-dominated and male-dominated society.
Likewise the racism expressed mainly in the form of Karl Linder was highly topical, and yet in this as in gender stereotypes the Younger family seem determined to fight for a better life, even going against the advice and warnings of both white and black communities.
The question of pride and the difficulties of finding pride in poverty, against systematic disenfranchisement, and cultural erosion is central to the complexities of this play.
Pride, for Beneatha, is a definite goal made especially complex for race and gender issues.
For Mama, it is something taken for granted, inherent in her sense of self yet embattled. For Walter, Pride is hypothetical until the end of the play, contingent on the attainment of a new financial station which is related to racial limits and ideas of poverty.
Sorry - it's a big question!
Lastly, you could look at generational issues. Mama has a more direct connection with the horrors of slavery and share-cropping, and this makes her more hesitant to engage with the white powers around her (Mr. Lindner, Walter's and Ruth's employers). Walter & Ruth represent the next generation that has bought into the American dream, and Beneatha is even more modern with her interest in her African roots.