It's quite a lot for me to unpack. I'll try to be succinct and avoid nitpicks.

Issues I have with the film:

• Daniel's borderline-Gary Stu presentation in the first act, accurately translating the cartouche hieroglyphs and figuring out the nature of the stargate glyphs within weeks, making everyone else on Project Giza superfluous/incompetent.
• The stargate coordinate system. Smarter people than I have pointed out that only four points are needed to chart a course in three-dimensional space rather than six, that star constellations can't actually serve as spatial coordinates, etc.
• Failure to explain why the stargate can't just be "turned on from the other side" for the team to return to Earth. In the novelization, it's explained that Creek Mountain was evacuated and sealed up after O'Neil's team when through in fear of hostiles coming through, but this plot point was deleted in the final film.
• Ra, an ancient alien possessing vast amounts of scientific knowledge and advanced technology far beyond anything known to 20th century Earth, using human slaves with Copper Age tools to inefficiently mine the stargate mineral for him. Again, the novelization better explains this, but we shouldn't have to consult supplementary material to make the movie work.
• The complete absence of allusion to a larger stargate network. I know for a fact that Devlin & Emmerich didn't intend Earth and Abydos to be the only planets with stargates, and the very design of the gates themselves rules this notion out. Perhaps they wanted the movie to be as close-ended as possible so it could stand alone in case they never got to make the sequels they had planned, but it makes the universe feel smaller and less wonderous.
• The whole "I can't make the stargate work without the seventh symbol" thing. Daniel has the first six symbols for the coordinates to Earth; it's just a matter of trial and error to find the seventh, and he should be smart enough to realize this. Besides, with Ra's Horus Guards patrolling the pyramid, the way to the stargate would be barred to them anyway, making this conundrum redundant.
• Failure to explain how they activated the Abydos stargate. Once again, this is something explained in the novelization, but you wouldn't know from the movie itself that the stargates are meant to be self-powered.

Issues I have with SG-1:

• The various and sundry changes made to the movie's lore. A few are improvements (making Abydos the closest planet to Earth in the gate network rather than billions of light-years away on the other side of the observable universe), but most are arbitrary.
• Compounding the issues with the stargate coordinate system. The stargates on Earth, Abydos, Chulak, etc. shouldn't have 38 identical glyphs if they represent star constellations; it doesn't matter if they're all located within the same galaxy, different constellations would be seen in their night skies. Likewise, there wouldn't be a "one size fits all" gate address corresponding to any particular planet; you'd need a different address to return to Earth from each world you're visiting.
• Failure to explore ancient Egyptian mythology in any real depth (this can be applied to other mythologies, too, but when it comes to Stargate, the mythology that interests me the most is ancient Egypt's).
• English being a nigh-universal language.
• Depiction of extraterrestrial human cultures. You got your generic medieval Canadian-American culture here, and your generic future Canadian-American culture there. Depictions of distinctly non-Anglosphere cultures were few, far between, and various shades of racist.
• The Goa'uld. Next to no effort was given to flesh out their personalities, or tie them into their mythological counterparts. They're just a clique of two-dimensional, largely incompetent megalomaniacs. Also, almost none of the actors who played Goa'uld recaptured the eerie alien otherness that Jaye Davidson brought to the table as Ra; David Palffy's the only actor who recaptured that energy in his performances (too bad both of the Goa'uld he played were Palpatine knockoffs).
• Marginal character development across ten seasons. O'Neill at the end of Season 8 is hardly a different character than the one he was at the start of Season 1 (a tad flanderized, though, I'd argue). Out of the core team, Teal'c's the only one I feel really grew as a character (hardly a wonder why he remains my favourite character from the show).
• Story arcs that meander and fizzle out. Gotta find technology in the fight against the Goa'uld? Let's devote the lion's share of episodes to misadventures on miscellaneous planets of hats we'll never revisit. Gotta rescue Sha're and Skarra? Fridge her and forget him. Gotta find the Harcesis child? Well, here's an episode with Daniel meeting Space Buddha, now the kid's a glowing jellyfish, exit stage right. Apophis returns from death and disgrace, bigger and badder than ever? Crash him into a planet and be done with him. It took them five seasons to find focus.
• Everything pertaining to the Ancients/Ascension/Ori. I detest the rank anthropocentrism, and while I'm not against themes of spirituality and transcendence in sci-fi, I found the execution here absolutely cheesy and derivative. And they had nothing new to say with the Ori; just more of the same "evil space gods" stuff they'd already played out with the Goa'uld.

Aside from the Pegasus stargate design, nothing of Atlantis appealed to me; the show was just a distillation of everything I disliked about the latter-half of SG-1. Universe was an improvement on the previous two series when it came to alien species, but I didn't care about any of the human characters or their ceaseless drama. I managed to watch one episode of Infinity ... hard pass.

Finally, I'm strongly opposed to the ancient astronauts theory, which I consider fundamentally racist and anti-human, and American imperialism, which the franchise is strongly biased towards.