Although Wonder Woman can fly has an invisible airplane. Also, you can see her while she's inside it, so I don't really get the point at all.
Edit: Apparently she couldn't fly at the time. The invisible part still doesn't make much sense. I guess she just wanted everyone to think she could fly? But sitting down?
That being said, I'm not sure that that's from the 1930s. That car has what I assume are supposed to be whitewall tires, which apparently existed in the 1930s but peaked in popularity in the 1950s. I'm no vintage car expert, but to me, the body styling looks more like what I get when I search for 1940s cars than either 1930s (cars were still boxier, didn't have a streamlined appearance) or 1950s (loss of the protruding tire guards or whatever those are called).
And I guess that the car alarm is probably anachronistic, but that that's intentional.