In the first wrestling scene, Sach wears shoes up until Hombre Montana lifts him over the ropes of the wrestling ring. Suddenly he's in his stocking feet. (In the following scene right after the match when Sach is revived, his shoes are back on his feet.)
The doors in Rhonda's apartment are stage doors - no latches.
The noise of Sach working out heard through the wall does not match the (lack of) activities within.