The Alternative Factor - S1-E28
Continuity mistake: Both the positive and negative versions of Lazarus have a long mustache and a fairly full "waterfall" beard - until the scene in the briefing room, when inexplicably, the mustache and beard are both suddenly so thin they're barely visible. As soon as they beam down to the planet, however, the much thicker facial hair is restored. (00:23:00 - 00:24:30)
The Alternative Factor - S1-E28
Continuity mistake: Mad Lazarus has just put a black-and-white hatch cover over the stolen dilithium crystal in his time ship. It's in place when Kirk arrives to confront him. But a moment later, when Kirk leans in and is accidentally transported to the negative universe, the cover has disappeared. It's still missing when Kirk returns to push Lazarus through the portal. (00:39:20)
The Alternative Factor - S1-E28
Continuity mistake: Kirk keeps referring to Masters as "Lieutenant", even though she has no braid on her sleeve - all Enterprise lieutenants have a single gold braid on each sleeve.
The Alternative Factor - S1-E28
Plot hole: Kirk knows that Lazarus is insane and that he wants the Enterprise dilithium crystals. Yet he's not restrained in sickbay and is, in fact, given free run of the ship so that he can knock out the crew in engineering and steal the crystals. Other than to further a woefully weak plotline, this makes no sense whatsoever.
The Alternative Factor - S1-E28
Continuity mistake: Lazarus' goatee and facial injures are constantly changing.
The Alternative Factor - S1-E28
Other mistake: When Spock calls Kirk to the bridge after he discovers the Lazarus energy source, he and Lazarus head to the bridge. There is a shot of McCoy standing in the corridor, and one of the red alert panels is burned out while the other is still flashing.
The Alternative Factor - S1-E28
Continuity mistake: Lazarus had knocked out the transporter technician, but when Kirk arrives he is fine and operating the transporter. (00:37:35)
Answer: Kirk was getting his physical and Dr. McCoy probably turned off communications, because if he hadn't, Kirk would have left and headed straight for the bridge, leaving McCoy irritated.