
This was one of my favorite TV shows from the late 70's. Sometime in the distant past I heard of an alternate order for the first season's episodes, and I want to capture it for reference purposes. Note that this is my version of the order, and may not match the version I heard. I only vaguely remember the original version.
I always thought of Space: 1999 as a kind of surreal-horror fantasy, rather than straightforward science fiction. In a way it is very Lovecraftian, in that Humans are alone in a strange and uncaring universe of massively more powerful beings. Using that guideline the problematic science is less of an issue.
I have two alternate versions which don't require much changing of the episodes. The first version assumes that Breakaway (the pilot episode) was the first episode. The second version assumes that Breakaway happened later in the series or not at all.
With the exception of two episodes, I can't stand to watch the second season of the show.

The first season of Space: 1999 was about the Moon leaving Earth's orbit, and the Alphan's desperate struggle for survival. In some ways the order of the first season makes more sense if the pivot point is "The Black Sun". All alien planet based stories happen after that episode.
The moon leaves Earth's orbit due to a terrible, man made, nuclear disaster.
While in route out of the system, an alien wandering in the solar system happens upon Alpha.
Because of the disaster, some of the Alphans take up mysticism and the occult, resulting in terror and death.
If Gwent kidnapped a human astronaut from one of the (very large number of) failed Earth space missions. Alternately, the Companion could have been an early Earth space scientist caught by his creation. Alpha intercepts Gwent before he can return to Earth and cause havoc.
On the outskirts of the solar system, Alpha discovers the horror that is responsible for at least one Earth space mission failure.
Now just outside of the solar system, Alpha encounters another wandering disaster. It is possible that the space spider caused the explosions on the Darius.
An old and dangerous earth space probe returns, followed by vengeance seeking aliens. Alpha intercepts this threat before it reaches Earth. I always wondered how they managed to have the knowledge of other planets that they mysteriously had, and if Voyager arrived here, then it makes some sense.
A second season episodes could fit into this order, if Maya was removed.
This could be considered a side effect of the black hole, or merely a hallucination of Commander Koenig.
Now the moon is an interstellar space craft. The black sun resides unseen, outside our solar system. If this was a naked spinning black sun without an accretion disk, then this might work. Alternately it could be one end of a wormhole. Note Bergman's use of the term "Black Sun" rather than "Black Hole" which was a known phenomenon in the late 70's. He could have meant a very different astrophysical situation than a singularity. Either way from now on Alpha is essentially traveling in a wormhole that flings them across space and time, allowing them to visit numerous alien worlds within weeks or months of each other.
This could be one side affect of approaching the black sun. This could also have been part of traveling through the black sun, or before hand.
This episode makes more sense after the Black Sun when looking at the "50 year" timeframe to return to earth. Alpha had only been traveling for a few weeks or months, but the aliens were planning on years of travel.
Alpha intercepts another set of Aliens, this time runaway criminals looking for a place to hide. The aliens don't seem to care that Alpha was related to Earth, perhaps because they didn't think of the moon as anything but another conveniently placed spacecraft.
Dr Russell's lost husband returns when Alpha visits it's first planet. Since the Alphans are shown performing landing protocol for the first (and only) time, this looks like the first real planet fall they have had. It could have been set up as a warning by the space brain.
Arra could be relating events like the Space Brain, Guardian of Piri, Last Sunset, and Last Enemy as part of their destinies.
The second planet the Alphans visit. With strange things happening which drive them away.
The Alphans get a surprise on the next planet, a long lost Earth space mission.
A planet is not at all happy to see the Alphans. Again this could have been related to the space brain episode, possibly as either a "remote" of the space brain, or as a "competitor".
The space brain finally makes it's appearance, with foamy results.
Another planet isn't happy to see the Alphans, but this time they try non-violent means.
The Alphans find a flawed paradise, and then destroy it by accident.
Worlds Beta and Gamma are very happy to see Alpha, but for the very wrong reasons.
The Alphans discover another paradise, but it doesn't want them any where nearby, and gives them a graphic and horrifying demonstration of why.
Alpha arrives at a dead planet and has to make a deadly decision.
A second season episodes could fit into this order, but after Testament of Arkadia so as not to cause too many problems with Maya.

It is also possible to put Breakaway later in the series, or ignore it altogether and never have the Moon leave Earth's orbit. If so, then the following episode order works, with some changes, and deletions. Most of these are Moonbase only episodes.
The only initial change would be for the first episode (which ever was chosen) to have the arrival of Koenig.
No changes needed.
No changes needed.
Change the explanation of Gwent and the companion as a lost Earth scientist and his experiment gone berserk.
Change the episode so that it isn't happening 20 years after the loss of the Ultra Probe, it happens only a year or so later with the arrival of the Ultra mission leader in the pod. He relates the story to the Alphans and the "Sargasso sea" of derelicts suddenly appears perilously close to Earth's orbit.
Since this is now in the solar system, the Darius will not be able to make it to Earth, and the Alphans only have a very limited time to visit the ship before it careens back into deep space.
No changes needed.
No changes needed.
No changes needed, this could have been explained by a "space storm" or something
The change would be to make the alien ship's life support deadly to the commissioner, so that he would be dead before the ship arrives on earth a day or so later.
The change would have to involve a reason for the criminals to choose the Moon rather than Earth, and not have quite so many massive ships.
If the lost space mission was found on Titan, and a little about why no one has been able to contact them
Change the space brain so that it comes by the Earth every 60 million years or so. Last time it caused the extinction of the dinosaurs.
Change the aliens so that they have a reason to land on the Moon instead of going to Earth. Since they need radiation and the Moon has two huge stockpiles of it, that shouldn't be too difficult.
Earth trains astronauts for the Meta Probe, and they are afflicted by an unknown disease.
Now that the Bringers of Wonder have pointed out a danger in the nuclear stockpiles, there are a couple of interesting possibilities. First the aliens could have already started to use the radiation dumps and indirectly caused the disease. Second, the aliens could have sabotaged the radiation dumps in case they were attacked by the Alphans.
The season cliff hanger could have been whether the Moon was going to be blasted out of Earth's orbit.

All photographs, images and text are copyright of Stephen Douglas 2009