By this stage in the series Helena and John are supposedly in some sort of (unconsumated) relationship, but despite Dione publicly propositioning John, Helena acts as if her ongoing relationship with him doesn't exist at all. (Note: It was obvious that Dione was just trying to gain his confidence, and Koenig was just playing along).
The moon has no atmosphere so when the Bethan gunship fires it's missiles over the moon-base towards the Deltans, there should be no noise, just flashes of light and maybe some vibration via the moon surface (but nowhere near as intense as is shown here). (Note: Gerry Anderson addressed this issue in the book "The Making of Space:1999", stating that "This is entertainment, and the age of silent movies is over." Even George Lucas didn't want to include sound in space on "Star Wars", but realized people expected it.)
When Dione is knocked down on top of Koenig as they both fall onto the floor due to an explosion, the actors actually start to fall down from a kneeling or crouching position, not whilst standing up as implied.
Dione is an alien from another planet, but somehow wears a motorcycle crash-helmet and leathers when entering Alpha and has some amalgam fillings in her teeth (shown when she screams). Both extremely Earth-like and Human things for a supposed alien.
It was out of character for Helena to have burst into Main Mission during Talos' attack on Alpha, shouting "John - the damage, the casualties, we can't take much more!" (There was certainly damage, but she later reports in the epilogue that the casualties merely amounted to five cases of middle ear damage - and not too severe. Possibly, her over-reaction could've been the result of ITC in New York insisting on more emotion from Barbara Bain for the tail end of the season - e.g., her overly distressed look when being dragged along by the Darians, and her over-reaction of the scarred face of deceased Dan Mateo).
When Dione radios Koenig saying not to give away the co-ordinates of her (stationary) spaceship to the Deltans, it doesn't occur to her that the very radio broadcast itself could be used by the Deltans to triangulate those co-ordinates via the TV receivers on their planet that they are talking to Koenig with.
Koenig looks directly at the sun via untinted binoculars when sweeping both planets on opposite sides of that sun at the start.