Galaxy Quest/WMG

The New Adventures of Galaxy Quest are real
Since it turned out that the interstellar community really does resemble the Galaxy Quest 'verse, the cast just took off in the spaceship in search of adventure, with a camera crew present to record "historical documents".

The computer is the Midnight Entity and has a weak hold on Gwen
Hence each feels compelled to repeat the lines of the other, with some paraphrasing.
 * ...Did you really have to bring the horror of that idea to the rest of us?

The Thermians have a Waaagh field.
This is why their society has no concept of lying - their beliefs shape reality. It's also why they could build a spacecraft using specifications from a television series that ran for four years and not only have it work, but have it work well, and build.
 * It also allows Quelleck to perform the similarly fictitious "stealth haze" to avoid capture.
 * He had a holographic disguise device, can stick to ceilings and knows the ship's layout. That might account for his stealth skills.
 * He also makes the maaktar chant of strength work though. It explains how things run on handwavium and, and also how Rule of Drama starts taking effect.

The US government knew of the Thermians
The United States of America knew alien threats existed out there. They knew Thermians liked Galaxy Quest and could build starships. The US of A guided the show and the fandom so it turned out like it did; and hey, at the end, they got a whole bunch of alien technology. Sure, just the escape pod, but the circuitry in the walls and the life support system are probably worth trillions. It also explains why a literal alien got a major role in a television show...

Jason Nesmith is responsible for the Thermian Genocide
Hungover, tired, and convinced he's just doing a bit for some fans, attacks Sarris's ship during the meeting that was supposed to be the Thermian's surrender. He alerts his superiors, who use it to justify wiping out the Thermian homeworld and possibly the Thermian space station. Because of Jason, an entire race will likely die out.
 * Saris was already in the process of conquering the Thermian home galaxy, and probably would have made quick work of them, had he not learned of the existence of the Omega 13. After Jason makes him look like a bitch after their first encounter, he devotes all his time to tracking down the protector, putting his plans for genocide on hold. Most of the Thermian race had already been wiped out. Jason might've inadvertently cost a few more lives (the space station?) but probably saved many more in the long run.
 * Also there's no evidence to suggest Sarris has superiors. He seems to be working on his own rather than representing a larger empire.

The movie is set in the same universe as Men in Black
Expanding on the third WMG from the top, the government actually did not know of the Thermians, but MIB did. Because the Thermians had transportation technology on par with the Star Trek transporters MIB had no way of tracking or preventing them from abducting the Galaxy Quest cast. At the end of the movie when the ship crashes into and destroys a large portion of the convention hall MIB confiscates the ship and neuralizes everyone in attendance. Because of this the Galaxy Quest cast are all deputized by MIB.

For Star Trek Movie Curse purposes, Galaxy Quest counts as the 10th film
It was released between Insurrection and Nemesis, and while the standard curse would have Nemesis and Star Trek XI be good and bad, respectively, the opposite is true. Thus, Galaxy Quest has become part of the curse, affecting how the counting works.

Alexander was screwed out of his earnings from the show's first run
Pay attention to the differences between his home and those of Gwen and Jason. They both live in (presumably) expensive houses, in nice areas, and very nicely decorated. Alexander, on the other hand, lives in less-nice house in a crappier part of town (as evidenced by the sound of police sirens in the background while he's talking with Gwen). He was one of the leads on the show; why can't he afford to live as nicely as Jason or Gwen? Either because he never earned as much as they did (a depressingly common phenomenon with British actors until the beginning of the 2000s), or because his financial manager mishandled his money.
 * Something I noticed that may contribute to this: Alexander is the only cast member who doesn't even try to hide how much he hates the show. The others at least pretend to be enthusiastic for the fan's sake. He just sulks and glares at everyone and makes his disdain for his character's catchphrase as clear as he possibly can without outright saying that he hates it. This could indicate that his memories of the show are far more unpleasant than the others.
 * Though part of his disgruntled attitude may be attributed to the fact that he's the only cast member who's got to wear prosthetics and make-up for his role.
 * If he was screwed out of his wages and was cripplingly type casted, that might be why.
 * And since Alex is based partly on Leonard Nimoy, then he was screwed out of his wages. Royally.
 * Gwen's house doesn't seem that lavish to me; it could just be a nicely-decorated apartment.
 * Agreed. It seems more like a male/female thing - both have apartments (as opposed to Jason's lavish beachhouse), but Gwen's decor is girly and pretty and Alex's is Classic Bachelor Who Doesn't Give A Shit.

Most Writers Are Human, but at least one that wrote the original Galaxy Quest episodes was not
If one or more of the writers already knew about the super-advanced technology that the Protector runs on, it would be easy for the Thermians to duplicate.

The "Space Station" the Protector debarks from is actually the remains of the Thermian homeworld
If you look carefully at the outside of the station as the Protector is flying away, you'll notice it looks like an asteroid or something similar, shaped vaguely like an apple core. It could be that it was actually the home of the Thermians, and that is all that's left after Sarris was done bombing the living hell out of it.

The Invention of Lying is set in the future of the Thermian race.
They found a new planet and settled in, and are still using holographic simulators to be people or figured out how to become biological humans.
 * Taking it further, the main character could be a descendant of Fred Kwan and Laliari. Come to think of it, "Laliari....