Has no one noticed that both scores I find at the International Music
Score project have the piano playing impossible (for modern pianos) Ab's
on score pages 72 and 73?
As for the issue of whether it's a one-movement work...well, he had
Liszt's comparatively recent model to follow, but Liszt's concertos have
fairly obvious movements. Prokofiev's first piano concerto is definitely
Lisztian in its form.
Where do those who hold to the multi-movement theory think that the
Tchaikovsky 3rd's movements begin and end?
Tchaikovsky drafted three movements, but only got around to
orchestrating the first of these (Allegro brillante) before his death. The
sketches for the Andante and Finale were later completed and orchestrated
by his friend Sergei Taneev, and these were published as a separate work.
Not all recordings of the Third Concerto include the Andante and Finale,
but you can find their scores on IMSLP here:
Interesting point about the A-flats, but as a non-pianist I can't give
an answer to that one :-)