The bridge has been shown to be fully manned, but close-ups of Spock at 2:46, 3:36, 6:20, 6:55, 7:45, 8:46 and 10:38 show an empty seat in the background.
McCoy enters the bridge with Dr. Sarah April. When the Beta Niobe Nova appears on the view screen, McCoy and Sarah virtually disappear (even though Sarah's voice is heard for a little bit). Commodore April is seen often, but neither McCoy nor Sarah for a long while. When Sarah finally appears again, she's in close proximity to her husband, as if they're inseparable, even though he's stood alone for quite some time. In a tumbling shot, the Aprils are shown standing right behind Kirk's command chair, where they were not seen shortly before. A panning shot at 9:42 from somewhere at Uhura's perspective shows neither April nor McCoy on the bridge. Suddenly, the Aprils are on the bridge. At 12:04, McCoy is finally shown again, standing behind the engineering station. At 16:43 when some time has passed, there's another overhead view of the bridge with no McCoy in sight - but who knows what to believe at this point?
Kirk mentions that there are 430 people aboard the Enterprise, as in Star Trek (1966). Under the economy of drawing the animated series (or hiring extras in the original), the viewer rarely, if ever, has a sense that there are more than 15 or 20 people on board.
When some of the crew change into smaller children, their clothes change size to match their smaller bodies.
No reason is given as to why the crew de-age so quickly. They were only in the negative universe a few days at most. While they would de-age, it would not even be noticeable. They certainly would not have become children. According to writer Fred Bronson, this is due to time dilation as the Enterprise races toward the nova: just as people age more slowly when travelling rapidly in the positive universe, the Enterprise crew de-ages more quickly when travelling rapidly in the negative universe.
In Karla Five's first message to the Enterprise, she speaks in reverse. Later, in her reverse-time universe, the crew can understand her (and her them) because, as Spock says, their brains are now in reverse. If this were true, then Karla's brain should likewise have been reversed when she entered the forward-time universe, allowing her to speak forwards.
When the Enterprise goes into the counter-clock universe, Kirk talks normally with the pilot who inadvertently dragged them into that universe, Karla-5. He says that he can understand her without the use of the universal translator. But it wasn't the UT that allowed him to understand her before; it only informed them that Karla-5 was speaking the same language as they were, only in reverse. It was the playback device which allowed for the reverse of Karla-5's message.
Dr. Sarah April is repeatedly addressed as "Mrs. April" by the bridge crew.