Martin Mystery/WMG

Martin Mystery is Johan Liebert
Well, for starters, both of them are blond-haired tricksters who enjoy annoying the hell out of their sisters, and on the top of that, they can't do physical harm.

Diana is under hypnosis by Lelouch
An explanation for her Face Heel Turn in You Do Voodoo and It's Alive part 1. Those episodes has Diana wearing sunglasses and mask respectively to hide the fact that she is under Lelouch's control.

Diana's Face Heel Turn in You Do Voodoo is one of Martin's scheme
The reason Martin taunts her in this episode is because he really wanted to see her becoming bad. By the way, the thing about Martin being insulted by her is just a cover-up so that nobody, except Java since he told him this while going to the Center, won't know that he planned on turning Diana that way.

Jenni didn't lose her memories of Martin's secret
In the episode "Journey to Terrorland", she is really immune to the memory erasing machine because Martin somehow did something to her. But she does find out that Diana is trying to erase her memories. Jenni angrily breaks up with Martin only to tell him that she can't be involved further; it could've happened without mind-wiping.

The main reason for Octavia being fired wasn't her evaluation
This WMG ties into a Martin Mystery fan fiction.

When Octavia was an agent, she was involved in something horrible put in place by the past leader of the Center, and when M.O.M replaced that leader, she initiated a purge of the Center. However, there was no direct link between Octavia and the crimes committed, so the only way M.O.M could get her out of the Center was to fire her through the evaluation, as a cover-up for purging her from the Center for her involvement in the crimes. This explains how despite being fired, she was able to build up her own organization, and the advanced technologies she had - the people working for her were also Center agents expunged during the purge, and the technology from the old regime was the technology Octavia used.

M.O.M. actually does have a family
To be more precise, she IS a mother, but in order to work as head of the Center, she had to leave her family. This is assuming that the husband knows about the Center, and actually was an agent for a time, but he retired to look after their child, leaving M.O.M to act as an agent, and eventually as the Center's head. This would explain how sometimes she treats Martin and Diana like her own children: to make up for her inability to be there for her own child.

Diana and Martin have spares at Torrington Academy
Not as wild as the rest of the WMG, but it makes sense. Martin and Diana have been shown to go off on Center missions during the school Lunch periods on missions. If they had classes in the afternoon, this would mean they're missing classes. By taking spares of classes that are likely double periods, or two singles, in the afternoon, this frees them up to go on missions, without really missing any school.

Obligatory NGE: This whole world is one of Shinji's alternate realities spawned during third impact.
Only this one actually still has Shinji in it. Watch "Attack of the Sea Mutants" (Season 3 Epiosde 6, Where Martin and Diana have to learn to be a team again). They  The boy looks just like Shinji.

The Center will be responsible for everything in Team Galaxy.
As evidence, I not only submit The Center's penchant for high-tech gear, but features in one episode M.O.M. testing a prototype flight suit that looks a LOT like the ones used in Team Galaxy. Right down to the shoulder-pads. Plus, The Center's already had plenty of dealings with aliens before, so it would make sense for THEM to step up as the go-between for humans and aliens in the future.