The dialogue refers to Elliot Ness as an FBI agent. He was actually a U.S. Treasury agent charged with enforcing Prohibition.
The US flag behind Roosevelt's desk has 50 stars. There were only 48 states in the 1930s.
President Roosevelt is shown as coming up with the New Deal after being inspired by Annie and her optimism. In reality, the New Deal program, including the name, was part of Roosevelt's 1932 campaign.
When the American Flag is depicted behind President Roosevelt and the other characters, the pattern is that of the current 50-starred Old Glory and not that of the 48 stars representing the 48 contiguous states of the Union at that time with its 6 rows & 8 columns of stars.
The flag in the background of the President's office is that of the current flag. However, this takes place in the 1930's, long before Alaska and Hawaii were states, so it should the flag with the design of 48 states, not 50.
When Warbucks and Annie come to the White House to meet FDR, they are introduced by a US Marine portrayed by a black actor. This takes place in 1933. The Marine Corps did not allow blacks until 1942.