A couple of "impossibilities" are detailed at the end that relate to the Amazing Stories August, September and October 1930 version.
There's an "Editor's Note" at the end of the version published at Gutenberg by John W. Campbell, Jr. (a fellow writer):
Editor, AMAZING STORIES:
Dr. Smith, in his foreword to "Skylark Three" mentions two errors
which he made knowingly. I think I can recognize the astronomical one,
at any rate.
Of course, the acceleration of twice 186,000 miles per second, as used
in escaping the field of the great "dud" star, as told in "Skylark of
Space" was impossible. Nothing could withstand that strain. Further,
no gravitational field could be that intense. It would have exactly
the effect Dr. Smith describes and allots to the zone of force in
"Skylark Three"--it would make a hole in space and pull the hole in
after it. Light would be too heavy to leave the planet. The effect on
space would be so great as to curve it so violently as to shut it in
about it like a blanket. The dud would be both invisible and
unapproachable.
The astronomical error? I wonder how Dr. Smith solved the problem of
three--or more--bodies? Osnome is a planet of a sun in a group of
seventeen suns, is it not? The gravitational field about even two suns
is so exceedingly complex that a planet could take up an orbit only
such that one sun was at each of the two foci of the ellipse of its
orbit, and then only provided the suns were of very nearly the same
mass, and stationary, which in turn means they must have no
attraction for each other. No, I think his complex system of seventeen
suns would not be so good for planets. Celestial Mechanics won't let
them stay there. And I really don't see why it was necessary to have
so complex a system.
[.......]
John W. Campbell, Jr.
Cambridge, Mass.
Credits: E-text prepared by Greg Weeks, L. N. Yaddanapudi, David Dyer-Bennet, and the Project Gutenberg Online Distributed Proofreading Team. Public domain in the USA. Rest of the World status unknown. Fair usage.
So, to sum up:
Faster than light travel without faster than light drive (besides, it muddles speed and acceleration).
A 17+ body-system that was posited as stable without the requisite qualification of appropriate star sizes and orbits.