When Will Rogers is addressing the bankers at 1:17:00 in, there are 2 old style microphones on the table in front of him. The one on the left of the screen, Rogers' right, is missing one of the suspension springs between the mic cartridge and the frame. It also has no wire attached to it, so it couldn't possibly function.
When Will Rogers leaves on his flight to Alaska in 1935 the plane that he and Wiley Post are flying is a Vultee BT-13 or -15 (depending on the engine used), an aircraft that didn't come into use until 1940. In the background as they are taking off are Boeing 377s (or C-97s), which debuted in the mid-1940s.