Factual error: Bill Kempt rigs the sapphire asteroid with rocket motors to divert it toward the Moon. The motors are old and cranky, and to ensure that they fire on time he must, at some risk, lash himself to the rock and manually start the ignition. Upon lighting the engines he has several seconds to cut himself free, but in the scene he's shown swinging weightlessly as he snips the cable. If the asteroid is accelerating, he ought not to be weightless, but rather should be hanging behind the rock on his tether.
Factual error: When Kempt disables the artificial gravity in the nightclub (to put his adversary at a disadvantage in the ensuing brawl), everything in the room is suddenly suddenly subject to the Moon's natural 1/6g. During the subsequent chaos there's a shot of a lady with her beverage dangling in mid-air. But even in 1/6g objects don't just float in place; they fall very definitely.
Factual error: Kemp's Moon ferry is essentially a kind of cargo carrying truck for making quick sub-orbital hops between points on the lunar surface. In the story the ship's services are hired for the purpose of attaching rocket engines onto a passing asteroid. This entails accelerating to lunar escape velocity, entering a solar orbit which matches that of the asteroid, dropping out of that solar orbit to one matching the Moon's, and at last braking its fall to make a soft landing. This amounts to an enormous total velocity change for the spacecraft's large total mass. The visible hull section available for carrying the propellant cannot possibly be carrying enough reaction mass to accomplish the mission.