When Professor Fate is lifted by an airplane flown by Max, the plane resembles a Curtiss Headless Pusher. This plane was not designed and built until 1912, four years after the year in which this movie was set. In July of 1908 Glenn Curtiss flew his June Bug design, which was the first public exhibition of flight in the US (the Wright Brothers had not yet flown publicly). The 1908 June Bug and the 1912 Headless Pusher bear little resemblance to each other. In reality, the June Bug was not as nimble and stable as the Pusher, so it is understandable why the 1912 design was used in the movie.
Note, the "June Bug" won a $2,500 prize for being the first aircraft to fly over 1km, on 4-July-1908
The "Curtiss Headless Pusher" (also known as the "Curtiss Model D"), initially had flaps in front of the pilot, which were later found to be unnecessary.
There's some video of a replica (with the "head") being flown here: https://www.youtube.com/watch?v=efOTxTixPBk
and another, from 2010 i Australia, made with a bamboo frame!: https://www.youtube.com/watch?v=oHrxxyBPaY4