As the 78 RPM record that plays during the "Public Enemy" scene ends, the needle can be seen entering the runout groove and hitting a terminal loop that goes in and out. This cyclical terminal groove was used on most 78s because some record changers of that era were would not trip (and play the next record) unless the arm moved in both directions. Because the record player in this scene was manual, the arm continued to oscillate, accompanied by a "whooshing" noise that was continued as the scene closed and the "Hawaii Five O" logo beach sequence segued into the next commercial.
McGarrett's Mercury is missing its rear-view mirror.
After the "Public Enemy" body is discovered, Mrs. Cramer, the landlady, insists on being called "Ms. Cramer", but 10 minuets later, Dano is still calling her "Miss Cramer".