IMDb.com says the "first airfield scene" was filmed at Grand Central Air Terminal in Glendale. IMDB has some interesting trivia about the movie, which apparently got very good reviews (for a 'B' picture) when it came out.
The use of several uncredited, but recognizable players in dual roles results in some odd situations: Sidney Bracey is first seen at the Burbank Airport starting point, then later he's in the crowd at Cleveland at the finish line.
Denny's plane that Janet flies in the race is a Cessna C-34 "Airmaster", registration NC15821. Made from 1935 to the beginning of WWII, a total of 228 of all variants were made, 42 being the C-34. According to FAA records, this particular plane is still registered to a private individual in the state of Washington (as of 2016).
The airplane named "Polly" is a Beech E17B made in 1937 with registration NC18044. As of 2016 this plane was still registered and airworthy. Fifty-four of this variant of the Beech model 17 were made out of 785 of all types. It is called the "Staggerwing" because the lower wing is forward of the upper on this biplane. Introduced in 1933 at a price of $14,000 to $17,000 depending on engine ($260,000 to $316,000 in 2016), it was a luxurious airplane for its time with a leather and mohair interior.
At the airport, Janet walks by a rare Arrow model F, registration NC17023, made in 1936. Only 103 were built between 1934 and 1936. It was a low-wing monoplane, powered by a modified Ford V8 automobile engine. Its initial price was only $1,500 ($27,000 in 2016).
The plane Denny and Stuffy talk over is a rare Buhl LA-1 "Bull Pup" made in 1931, registration NC352Y. Only about 100 were made from 1930 to 1932 when the company went out of business due to the Depression. According to FAA records, this particular plane is still registered to a private individual in Oregon (in 2016).
The plane that Kit flies in the race is a Ryan ST-A, made in 1937, registration NC17344 - which was canceled in 1948, fate unknown. First flown in 1934, 73 of the ST-A variant were built, out of a total of 1,568 of all types
Some great names in the cast, including Victor Jory, Eddie Foy Jr., Maxie Rosenbloom, William Gargan, Eve Arden (TV's "Our Miss Brooks") and Frank Faylen ("Herbert T. Gillis", "Dobie's" dad).