Both Bergman and the Bethans state that because the two planets always have their star between them, they cannot directly shoot at each other. It is common practice today to slingshot space probes around celestial bodies, using their gravity to alter velocity and course, what's known as a "gravity assist" maneuver. A straight line course between planets is not necessary. That is, assuming their advanced missiles inexplicably had no guidance systems that could correct their course in mid-flight and they were just firing blindly.
Whenever missiles are fired on or at the Moon, Koenig gives the order for everyone to get down on the floor away from the windows. However, if the explosions had damaged the windows, the escaping air would fling the glass outward, as seen in other episodes. Their bigger problem would have been Main Mission instantly decompressing and killing them all.
The foam like substance that threatens to crush Alpha (and the Moon) gets its look from the fact that the SFX crew resorted to soap bubbles for creating the effect.
Whereas most of the music heard on Space: 1999 was composed specifically for the series, in the Space Brain episode we can hear extracts of Gustav Holt's orchestral suite "The Planets". This happens towards the end of the episode when it is uncertain if the Moon will survive going through the Brain.
Another addition to Mr. Gray's score is Remo Giazotto's composition 'Adagio in G Minor for Strings and Organ in G Minor' it is played over the flight sequences of the Ultra Probe.
Throughout the episode, the buttons on Keonig's commlock are misaligned.
Kano orders Eagles 9 and 19 to landing pad one, but there is only enough room on the pads for one Eagle at a time.
In one exterior shot of Alan's Eagle, it shows only one pilot, but Alan has a co-pilot with him.
The close up shots of the Eagle front module show the Ariel probe to be in a slightly different position than it is in the longer shots.
A false assumption is that Alpha's windows could all be slid open, which would have made no sense on the airless moon. But only one window had a visible handle to open with, and Koenig used it after the atmosphere had been established and Alphans were frolicking on the surface. So the window could easily have been retrofitted afterwards, rather than having existed all the time. All of the windows visible in the last scene showed no handles.
As the Eagle is loaded with supplies, people are entering from both port and starboard docking ports, but the exterior shots of the Eagle show it is only docked on the starboard side.
As the Eagle returns to Alpha, Sandra Benes is clearly seen in Main Mission--she even has a line. Shortly afterwards, the Eagle crashes and she is seen unconscious inside of it.
In Koenig's dream, as he walks down the steps from his office to Main Mission, a studio light is briefly visible in the top right corner of the picture.
In Koenig's dream, his name was spelled incorrectly as "Keonig" in the close up of a monitor screen. It was, however, correct in the wider shots of the same screen.
After the cockpit section of Eagle 1 is detatched, the open door inside still shows the rear rooms of the Eagle's main body.
The door in the cockpit of Eagle 1 bears the number 4, but when Alan goes to open it, the number is now 6.
Dr. Mathias examines Dr. Russell when she returns, and says her blood pressure is "80 over 120" and declares it normal. He has the numbers reversed: 120 over 80 is normal.
As Helena looks at her thermograph, she is looking at it backwards as her name can be read from our (the camera's) position.
The third Eagle is shown with the docking tube connected to the starboard side, but it launches with the tube on the port side.
Koenig had Alan cut the Eagle's engines, but the switch used to do so was clearly on his side of the cabin so it would have been quicker and easier for both of them if he did it himself.
Koenig tells Paul to try to make contact using sound, light, and radio wave patterns. However, as sound cannot travel through the vacuum of space, it was pointless to suggest it.