When Ted Clifford hacks into Main Mission's computer, Sandra says, "What's he doing? He doesn't know anything about a computer." This statement is ludicrous. There is no way that Clifford could have anything to do with the space program without having training in computers. As will be seen in later episodes, it seems as though all men aboard Moon Base Alpha can pilot an Eagle, and the cockpit is filled with computer instrumentation. Most certainly, Clifford would, or should have gotten Eagle piloting training.
The sound of Carter's Eagle skidding along the lunar surface continues after the ship is shown to have come to a stop.
Considering the technology employed on the Moonbase, it's highly unlikely that Ted Clifford wouldn't know anything about operating a computer, as Sandra had stated.
At 3:57, when they switch on the main screen, it shows the moon from an angle out in space where no cameras exist that the Alpha base could access. (Note: Supposedly there are (never seen) satellites orbiting the moon).
The episode's biggest plot hole involves the Alphan's mysterious knowledge of the planet Triton's location and sudden demise (Victor even being familiar with the planet's name) which Alpha's computer was unaware of. Koenig claims that Triton was located 2 million light years from their current location. Not only would it be unlikely that they would have any knowledge of a planet that far away, but that distance would place the planet outside the Milky Way galaxy. The episode's novelization by E.C. Tubb solves this by Triton being the moon of Neptune.
As Koenig is leading a rescue party to the crashed Eagle, Mathias informs him over communications that one of the two pilots, Donovan, is dead. Later, however, in the Medical Center, after recovering from his ordeal on the moon's surface, Koenig asks about Donovan's condition.