Just after the first time that Kirk uses the universal translator to speak with The Companion, Kirk, Spock, and McCoy turn to walk into Cochrane's shelter, which they were standing less than 10 feet away from, while Cochrane is at least 50 yards away. When the shot switches to the interior, Kirk, Spock, and McCoy are seen coming through the entry door, immediately followed by Cochrane, even though Cochrane would have been 30-45 seconds away at normal walking speed.
The shuttle craft used is called the "Galileo". The Galileo was destroyed in The Galileo Seven (1967). However, the Enterprise would have put in for re-supply at least twice in the time since then. "Galileo" was simply replaced.
The Companion acts as if she has never felt loneliness before. Loneliness is why she abducted Zefram Cochrane in the first place. However, loneliness felt as the Companion and as felt as a human being are obviously very different.
When Cochrane communicates with the entity the first time, he is shown from one angle, with two types of trees on either side of him several feet away. When the entity leaves, Cochrane is shown from the opposite angle, with different trees much closer to him.
In the shot where Cochrane first arrives at the Galileo, the black edge of the set is clearly visible behind the shuttlecraft.
When Cochrane runs up to meet Kirk and the others, the glare of the stage lighting is barely visible from the top.
The Companion rejuvenated Cochran when he was dying and made him young again, and when Kirk is first speaking with the Companion it tells him they too will remain unchanged on the planet. But Commissioner Hedford remains ill until the Companion melds with her.
The Companion fries much of circuitry of the shuttle. At the end, she says the captives are free to go, but it is impossible for her to have repaired all of those components.