Dewey Decimal System. This becomes kind of a running joke for several chapters. Jem has previously told Scout that Miss Caroline's teaching style is based on the Dewey Decimal System, but he is confused: The Dewey Decimal System is a library organizational numbering system originated by Melvil Dewey; Miss Caroline has studied the progressive educational philosophies of John Dewey.
Duncecap. A duncecap is a type of conical (cone-shaped) hat that children were made to wear in class when they misbehaved or when they gave incorrect answers. Along with the duncecap often came a stool on which the child sat--usually in the corner, in which Scout had to stand in Chapter 2.
Wrigley's Double-Mint. A type of gum, perhaps the most popular brand in the 1930s and still popular today.
Indian-head pennies. American pennies minted from 1859-1909.
"Finder's keepers". "Finder's keepers, losers weepers" is an old adage dating at least as far back as Roman times that relates to when an object is lost or abandoned and then found, it belongs to the person who has found it.
Twins hitched together. Dill claims to have seen a pair of Siamese twins.
"In a pig's ear." A variant of "in a pig's eye," this is an idiom which expresses extreme disbelief.
Rover Boys. Jem's and Scout's favorite literary serial, which first began in 1899.
"I'll knock you bowlegged." I know several people who still use this saying, which is simply an idle threat of violence that, once enacted, will result in the recipient having "bow legs"--legs which are rounded to the outside instead of being straight, like an archer's bow.
One Man's Family. This radio soap opera was still a novelty during the early chapters of TKAM. It eventually ran for 30 years, beginning in 1932.
"I'll tan you." This is a threat by Atticus that the children will be spanked or whipped if the newspaper has been cut up before Atticus has read it.