After Mannix snatches his guard's gun & hurls it at him as he drinks tea, it lands on Dorso's desk by his left arm, his hand down off the desk's edge; but when Mannix leaves after slamming the guard's shoulder holstered weapon as having gone "out with running boards," Dorso's whole arm and hand are resting on the desk edge & the gun is gone.
After Mannix talks to Valerie Price and leaves the Opal Club, Charlie makes a call from a public phone. The number he dials is 222-2222.
At ~45min in as Mannix gets off the elevator to storm into Carl Dorso's office, the camera is shaking so hard that not only does it appear that an earthquake is taking place, but a good bit of the soundstage is revealed directly above the door to Carl Dorso's office just before Mannix barges in.
When the woman who helps Mannix hide in her apartment is accosted downstairs by the bad guys pursuing him, she tells them that he's not up there, but they run up to her apartment anyways, to check. However, she never told them in which one she lived, and they made a beeline for it, opening her door in less than a minute, as she also conveniently did not lock her front door, knowing that the bad guys were after Mannix. Both were highly improbable goofs.
When Joe arrives at Harry Armitage's apartment building, he is stopped by a police officer as he tries to board the elevator. As Mannix explains why he needs to go up to Armitage's apartment, the shadow of the boom microphone appears, and moves around, on the wall above and behind the police officer's head.
When Mannix cuts Hackett by saying he "still ha(s) nothing - except money," Hackett in his laughing reply mispronounces his name as "Mannick."