Good question. I'll attempt to name a couple of thematic similarities between the two pieces.
Race and racial issues -- Race is at the forefront of "To Kill a Mockingbird." Tom Robinson is on trial for rape, and through the trial, Atticus is able to show that Tom is innocent. He is still convicted, though, as a scapegoat. That was only possible back then because Tom was black. Similarly there are race issues within "The Merchant of Venice." It's not a black/white issue though. It's a Jew/non-Jew issue. Perhaps you could claim that's not racial, but religious, but Judaism is a blurry line between race and religion. Shylock is portrayed as the play's "bad guy" and happens to be Jewish.
The theme of justice is another solid connection between the two. A court trial is at the forefront of both plots. One is for rape; the other is for financial reasons. But in both cases, the authors emphasize the importance that proper justice be done. What's odd to note though is that Lee has Atticus do everything 100% correctly (even shows Tom's innocence) and still loses. Shakespeare, on the other hand, has Portia being quite devious in court and legally getting the win. She doesn't technically win or lose, though. Shylock more or less gives up and leaves. While justice is central to the plots, both pieces leave the reader feeling like justice was not attained.
Similarities between the narratives of To Kill a Mockingbird and The Merchant of Venice are the motifs of culture clashes and stereotypes of cultures.
Specifically, within the time/setting of The Merchant of Venice, there are attitudes and practices that are customary for the Venetian merchants and others for the Jewish merchants and moneylenders.
Just as Bob Ewell is a stereotype for the shiftless, lazy, ignorant, backward "red-neck" who adheres to a culture of racism, Shylock is also presented as a stereotype. There are some traits that Shylock exhibits which are based upon prejudiced conceptions of his race, faith, and customs.
Because the Jews are not indigenous to Italy, they are not treated in the same manner as are Venetian citizens in the play. They live in certain parts of the city of Venice, having been moved into ghettos constructed to confine them. So much like Bob Ewell, who lives at the end of the "Negro section" of Maycomb, Shylock is not viewed favorably by the citizenry of Venice because of the "culture clash" with the Christian Venetians; he is isolated.
In the Jewish culture, pork is considered unclean and is not to be eaten. When, for instance, Bassanio invites Shylock to eat dinner with him and his friends, a repulsed Shylock responds,
...to smell pork? I don’t think so! Your prophet Jesus sent the devil into a herd of pigs. I’m not going to eat that. I’ll buy with you, sell with you, talk with you, walk with you, and so on, but I won’t eat with you, drink with you, or pray with you. (1.3.27)
Bob and Mayella Ewell also feel umbrage as they clash with the educated Atticus Finch and Judge Taylor in the courtroom. Reacting to the Atticus's questions on the witness stand, Mayella lashes out,
"...if you fine fancy gentlemen don't wanta do nothin' about it then you're all yellow stinkin' cowards, stinkin' cowards, the lot of you. Your fancy airs don't come to nothin...."
We can easily imagine that both Mayella and Shylock lash out in defense; they have learned from experience to be wary of any kindness extended from the people who so regularly treat them with contempt.
Certainly, the members of the more respected class/culture of Maycomb and of Venice represent stereotypical views. Aunt Alexandra and Mrs. Merriweather are disdainful of the lower social class; similarly, Signor Antonio has been known to deride Shylock. For instance, when Antonio asks to borrow money because Bassanio needs it, Shylock reminds the merchant of his insults:
In the Rialto you have rated meAbout my moneys and my usances.Still have I borne it with a patient shrug,For sufferance is the badge of all our tribe.You call me misbeliever, cutthroat dog....(1.3.105-109)