The first involves how physical evidence at a crime scene was collected and stored. The science of forensic investigation was just developing in the 20's and 30's and it was common for items to be "bagged and tagged" in regular brown paper bags and cardboard boxes. While my familiarity with period police work is admittedly limited, the Lindbergh case is the first one I've come across where evidence, in this case human remains and items from the immediate scene, was stored in glass bottles:
The second involves the use of silver nitrate to highlight fingerprints that were unrecoverable using traditional powder techniques. It sounds like something from "CSI", and a refined version of the technique is indeed used today, but it dates back to the start of the 20th century:
Early documentation reveals that the silver nitrate process was developed in the 1910's. In 1918, the IAI Conference gave a presentation on this process. Different people were experimenting with it but it's development is historically credited to Dr. Erastus Mead Hudson. The silver nitrate process became well known after Dr. Hudson recovered latent prints on a ladder used in the Lindbergh kidnapping case (1932). In later years, Dr. Hudson did additional research with the New York Police Department exploring other possible uses for the silver nitrate process, such as recovering latent prints from cloth and gloves.
Finger Print and Identification Magazine, Vol. 17, No. 3, September 1935. The Federal Bureau of Investigation has also taken credit for the development of silver nitrate. They claim that it was first used in 1933 in the William Hamm kidnapping case (the president of the Hamm Brewing Company).