So here's how I would have done the film. After all, complaining is easy but being constructive is real work. If I don't describe it, assume I would have left things as they were in the canonical movie. Here there be spoilers, so be ye warned...
In General
*If I were making the movie back then, I'd be a lot more sparing with the CGI and use practical effects as much as possible. Yes, CGI is cheaper than physical props (unless you're using computer-destroying amounts of hyper-realistic effects like Transformers: The Revenge of the Fallen, which apparently caused one of the computers to catch fire when rendering), but one of the biggest flaws in the canonical film was how poorly the special effects have aged. In comparison, Hellraiser and Pumpkinhead with their models and puppets have aged far better.
Today is a different story, but the kind of effects the Transformers series had are quite expensive. Using practical effects when possible might be a way to save money rather than the "spend money to make money" it would have been in the early-mid 1980s.
And now onto the storyline...
Act I
*The opening section showing Alex's life in the trailer park, how he gives up an adventure with Maggie and his friends to help the residents, etc. is good as it is. It does a good job explaining his helpful character, the dullness of his small-town life, etc.
*When the hologram of Xur confronts his father, I would given him more motivation for his treason beyond what seem to be megalomania and Daddy issues. In his ranting he can complain about how weak the Star League has gotten, how his "movement" would have revitalized their civilization (and his father's response could imply that this "cult" is more like a Nazi movement), and how the fact the Star League can find only a few dozen warriors to contest the Ko-Dan fleet proves him right. When Enduran tells him his "cult" has been suppressed and scattered, he can just smirk knowingly. This would provide a stronger implication than the canonical film that the saboteur who cripples Starfighter Command's defenses was a Xur loyalist.
*I liked the canonical arrival of Centauri. However, I'd have used less CGI and more practical effects for the car that turns into a spaceship. Furthermore, Alex seems very...subdued throughout the entire abduction by Centauri. I would have depicted him at various points as being frightened, bewildered, and awestruck depending on where they are in the journey--fear when it turns into a kidnapping and it's revealed Centauri is an alien, bewildered when the car suddenly turns into a spacecraft, and straight up in awe at seeing Saturn and going into hyperspace. He's too calm and nonreactive throughout this entire adventure and that needs to change. If Lance Guest can act to the appropriate level, great, but if not, recast him.
*I would have depicted the Starfighter base being well away from Rylos itself and kept the sabotage of it defenses by (presumably) one of Xur's cultists. Rather than have the carrier launching rocks, I would have the destruction of the base inflicted by the Ko-Dan equivalent of torpedo bombers (fighters armed with heavy missiles) in the vein of the Japanese attack on Pearl Harbor (see the Michael Bay version here from the film Pearl Harbor) or the Cylon attack on Colonial military bases in Battlestar Galactica. It would take a very long time for rocks thrown from a capital ship to arrive at a fixed targets and they'd be tracked and attacked all along the way. A swarm of fighters armed with long-ranged missiles would be a much more flexible, dangerous opponent. One could see the Starfighters massacred as their crews rush out to man them, a few successfully launching and getting shot down before they can orient themselves, and perhaps one or two lucky or skilled ones who can drag a few Ko-Dan into the abyss with them. Then the Ko-Dan fleet leaves the ruined base behind to advance on Rylos, allowing Centauri to flee to Earth in a surviving ship to collect Alex.
Act II
*Although in my review I said that "Beta Alex's" social ineptitude was painful to watch, that might be a personal tic on my part. Given how well Beta Alex can mimic Alex's voice and mannerisms (including his attitude toward his little brother) simply by having touched him before taking on his likeness, it seems inconsistent that he wouldn't know about Maggie's relatively forward sexuality (i.e. sticking her tongue in his ear out of nowhere) or need to eavesdrop on one of Alex's friends in order to whisper sweet nothings into her ear. Maybe when the real Alex gets slapped by Maggie and confronts Beta Alex about the issue, Beta Alex can state that they weren't in contact long enough for him to get the full package of memories or something like that.
*When Alex makes the obvious suggestion that the Star League use the "simuloid" technology to make copies of its pilots Beta Alex-style, Beta Alex said they're not allowed to fight. Given the concerns the Star League might have about aggressive artificial intelligence (think SkyNet from Terminator or the Cylons from the Battlestar Galactica TV series), that might merit a bit of explanation. Maybe Beta Alex can say something like, "The last time they tried that, there was an uprising. We're not allowed to fight anymore" or something like that. If Beta Alex displays obvious hesitation in taking on the alien hit-man later, that could show him overriding anti-violence programming by sheer willpower to protect the Star League.
*The subplot with the pair of alien "hit-beasts" sent to kill Alex and how Maggie and the simuloid foil their plan--at the cost of the simuloid's life--stays. I'd re-do the "I love you Alex Rogan" bit from Maggie to be a bit less goofy though. Once Maggie learned that Beta Alex wasn't actually Alex and there was an alien war on, that subplot got a lot more fun.
Act III
*The scene where Alex and Grig are showing one another pictures of their families and Grig's picture of his wife was basically him wearing more feminine clothing was unintentionally hilarious. To a human with little experience of aliens all members of Grig's species might look the same, but that sort of realism damages the quality of the film. The family-pictures sequence is a good thing in general, but it should have been done a bit less goofily.
*I'd keep the general scenario where Alex and Grig's Gunstar powers down to let the Ko-Dan carrier pass, then ambushes it and destroys its communication system. And keep the "death blossom" as well, since that's such a distinctive part of the movie.
*Given Alex's self-sacrificing nature, perhaps the Gunstar is damaged during or after the death blossom and he and Grig try to kamikaze the Ko-Dan carrier? Even with its fighters wiped out, it might still have orbital bombardment weapons or troops to invade Rylos with. Grig is messing around with the circuitry like he did in the canonical film where they were running into power problems and manages to pull out of the terminal dive. Then they unload the last of their weapons into the carrier at point-blank range, inflicting some kind of terminal damage on it (like the destruction of the Executor's bridge in Return of the Jedi perhaps, minus the successful suicide). This would allow for Xur to escape like in the canonical film.
*I would tone down the crash of the Ko-Dan carrier into Rylos' moon. The way it's depicted, the carrier is almost as big as the moon is and the explosion is so ridiculously massive that one would think it would do significant damage to the moon itself. It doesn't--we have the carrier crash, the ludicrous explosion, and the moon surviving unscathed. Rather than seeing the carrier collide with the moon from Alex's point of view, I'd have cut to a closer shot of seeing the carrier crashing into the surface of the (much larger) moon and exploding, albeit in a less over-the-top way. This is where models and practical effects would be particularly useful.
*When the Gunstar lands in the trailer park, I would have depicted the townsfolk as being a lot more anxious, afraid, and (once Grig appears) more aggressive. Alex is able to calm them down and Grig's attempts at friendliness reflect well on him, but I would have toned down the older women's friendliness toward him immediately after they're all calling him "monster." Seriously, it came off as almost romantic on their parts. The movie doesn't need Grig to become the alien player of the trailer park, however amusing that concept might be. The interaction between Alex, Maggie, and Maggie's grandmother is good, so that needs to stay.
*And then ending where Louis starts playing the arcade game after his brother and future sister-in-law leave Earth is perfect. That stays.
*And then ending where Louis starts playing the arcade game after his brother and future sister-in-law leave Earth is perfect. That stays.
However, there's a big enough world depicted in this one that it could easily be adapted into a television show. Think a cross between Star Wars and Game of Thrones.
The storyline of the original movie could easily be the first season of a television series, with the battle between the Gunstar and the Ko-Dan Armada being the climax of Season One and Alex returning to the trailer park for Maggie ending the season (along with seeing just where Xur ended up). Season Two could be Alex training the next batch of fighter pilots, Maggie adapting (or not) to this strange new world, the Ko-Dans' next move, and some scheming and shenanigans by Xur and whatever cultists he still has. An expanded television adaptation would allow for more back-story for the Star League, Xur and his treason, and the Ko-Dan. In particular, the Ko-Dan admiral and his staff, who clearly dislike having to deal with Xur and have the courage to face death unflinchingly when the carrier crashes, can be developed as more interesting characters.
Pity the writer is being so stubborn. If I had a great idea that was adapted into a cult classic and someone came to me decades later with the offer to make it into the next Star Wars, I might insist on being involved in the process but I'd let it be done.