How fast was the moon travelling to meet a new civilisation every week yet slow enough for them to have time to fly back and forth to them?
Its the basic premise that concerns me. I suppose maybe they went through a black hole or something every week conveniently in their path. Still if you ignore the improbability of their travels through space the rest of it was fun.
The thing is, the first season of Space: 1999 wasn't supposed to make logical or scientific sense. It was surrealist/existentialist fantasy using space as a metaphor, an unknowable realm that challenged our beliefs and rendered our certainties meaningless. The fact that the events Moonbase Alpha experienced made a mockery of our understanding of the universe was intentional. You might as well nitpick the science of Gregor Samsa waking up as a cockroach. Being inexplicable was the point.
Although if you want to look at it more literally, the pilot episode did have brief dialogue implying that the unprecedentedly huge nuclear reaction/explosion at the dump site was generating some kind of magnetic/gravitational effect never seen before and never predicted by science. The suggestion was that it was producing a sort of antigravity field that severed the Moon's gravitational ties to Earth. One can presume that it also functioned as a kind of warp field.
By contrast, season 2 was just silly and nonsensical and conceptually random. But they did throw in a token reference or two to the Moon falling through random space warps from time to time.