Accidentally Correct Writing: In "Orpheus" Jack mans a sniper rifle during a rescue operation against a Goa'uld P.O.W. Camp. He aims for center of mass. Falls here because the showrunners' reasoning for doing that was because headshots are messy and they didn't want to have to argue with the network censors, but trained snipers in real life usually aim for center of mass because it's a bigger target.
Amanda Tapping played multiple Carters in several different episodes. "Point of View" has Dr. Samantha Carter, "Gemini" features extended interactions between Carter and RepliCarter, and "Ripple Effect" features over a dozen Carters in a single scene. Lampshaded when General Landry calls out for Carter, and everyone stares at him.
"Tin Man", where the alien Harlan creates robotic duplicates of SG-1. They reappear in "Double Jeopardy", where the two O'Neills get into a fistfight.
Guest star Dom De Luise (briefly) as the title character and his creator in "Urgo".
Starting in season nine, Ba'al began cloning himself, with Cliff Simon playing multiple Ba'als in several episodes.
The show was fond of making MacGyver references — which of course, leads to Celebrity Paradox. Lampshaded by Amanda Tapping in a blooper shown in the 200th episode special "Inside the 200th Episode". O'Neill is from Minnesota, the same state MacGyver is from (also Richard Dean Anderson's home state). Like MacGyver, O'Neill is an astronomy enthusiast (MacGyver was shown living in an observatory in the pilot of his TV show). An inversion: Jack likes having a gun and will protest whenever he's told to not carry one, while MacGyver did not like guns and was known for avoiding their use. Like MacGyver, O'Neill is an avid fisherman. Both MacGyver and O'Neill are shown to be hockey fans.
The name of his character is also probably a Shout-Out, as Jeffery Combs was a prolific actor in multiple Star Trek shows, including Deep Space Nine (Weyoun, Brunt, others) and Enterprise (most noted for Shran, but also others).
Patrick Mc Kenna guest-starred in "The Other Guys" and "Avenger 2.0" as Dr. Jay Felger. In the latter episode he was seen putting a roll of duct tape into his backpack. DVD commentary confirmed this was a Shout-Out to The Red Green Show, where McKenna played Harold.
When Vala is pitching story ideas to Martin Lloyd in "200", he immediately recognizes her pitches as retreads of classic stories, including The Wizard of Oz and Gilligan's Island. He recommends that, if she is going to rip off something, make sure it is something nobody has ever heard of. Her next suggestion is Farscape, the series she (Claudia Black) and Mitchell (Ben Browder) had previously starred in before joining SG-1, with Claudia reprising her role as Aeryn Sun (Browder did not appear as John Crichton, but instead as Stark, while Michael Shanks was Crichton, in a meta-reference to the resemblance between the two actors). Martin admits that he had never heard of that one.
When the one-off character Alec Colson, played by Charles Shaughnessy, enters the Alpha Site, the first person he's introduced to is one Captain Sheffield.
Dwight Schultz plays The Gamekeeper who runs a virtual reality simulation and insists that the inhabitants never leave it. On Star Trek: The Next Generation, Schultz played Lt. Reginald Barclay who spent all his free time on the holodeck and was afraid to leave it.
"Citizen Joe" features Dan Castellaneta as the titular barber, and he openly agrees with O'Neill that Mr. Burns is a Goa'uld. Homer Simpson would know better than anybody, right?
Ascended Fanon: Originally Jack and Sam were never supposed to develop romantic feelings for each other. When the Jack×Sam shipping started in the fandom, the writers noticed that they had the chemistry for it and threw it in.
Backed by the Pentagon: Particularly the US Air Force. Multiple real-life Air Force Chiefs of Staff have appeared on the show, playing themselves. Other branches became involved on occasion, and the US Navy loaned them a submarine for "Small Victories." And again for the movie "Continuum".
The text on the back of the DVD cover of the Swedish release of "Children of the Gods" (DVD release of the pilot episode) claims that the villains of the movie are Ra, "the brutal Goa'uld", and General Hammond. This is very not correct.
Creator Backlash: Roland Emmerich and Dean Devlin, the team behind the original movie, have had less than kind things to say about the TV series overall, which is why they refused to get a "created by" credit for it, and at one point planned to make a direct sequel to the film that would have completely ignored the TV series just to spite it.
Defictionalization: There is a door in the real-life Cheyenne Mountain Complex labelled "Stargate Command", which some sources say has six locks and a guard placed next to it. Whether or not the locks and guard are really there, the door itself leads to a broom closet.
Doing It for the Art: One of the "flashbacks" from "200" features an incident where O'Neill was rendered invisible; one of the scenes features him walking down a hallway and talking with Teal'c, but since he is invisible he can only be located by the coffee cup that he is carrying at the time. The plan was to have one of Richard Dean Anderson's stand-ins or stunt-doubles actually perform the scene, since it would require wearing a full-body green suit in order to have the body edited out in post-production, but RDA insisted on actually performing the scene himself. You still cannot see him, since he is invisible, but hopefully you can just tell that it is really O'Neill walking with Teal'c.
Executive Meddling: Sha're being in the nude as she is implanted with a Goa'uld symbiote in "Children of the Gods" was a result of Showtime executives who wanted the show to appeal to adults, against the showrunners' intentions. This is why the scene was Edited for Syndication in later airings and internationally along with the 2009 Re-Cut completely remove the visible nudity as a result.
Fake American: Filmed in Canada but primarily set in the United States, so a large segment of the cast. Amanda Tapping in particular was born in England and raised in Canada.
Replicator Carter is frequently compressed to RepliCarter.
"Fargate" for the retooled Seasons 9 and 10, due to it having two of the Farscape actors having main roles in the show.
Follow the Leader: The short-lived Season 4 character Anise/Freya was intended as a "sexy female alien" to compete with Star Trek: Voyager's Seven of Nine. Vanessa Angel, who played Anise/Freya, had even auditioned for the part of Seven of Nine.
Amanda Tapping was pregnant throughout the end of Season Eight, with her stomach hidden with the traditional practices of obstructing objects and dark, black clothing. She was on maternity leave when filming began for Season 9, leading to Carter being temporarily assigned to Area 51.
Lexa Doig became pregnant with her and husband Michael Shanks' second child during filming for Season 10, resulting in her character of Dr. Carolyn Lam having a greatly reduced presence and all but disappearing from the show.
Brad Wright was not very proud of the full-frontal nudity in "Children of the Gods", which is why he did a Re-Cut in 2009 to remove said content.
Not the series itself, but the disintegration feature of Zats. The writers have frequently mentioned in episode commentaries what a bad idea that was, to the point where they mock it in-universe in "Wormhole X-treme!".
The first-season episode Hathor, to the point it's borderline Canon Discontinuity. Much of what was established in the episode was quietly retconned, and while Hathor herself returned to be Killed Off for Real at the end of Season 2 and start of Season 3, the only other reference made is in Heroes, where Janet is going over O'Neill's medical history in the SGC with a documentarian, and sets aside one file stating "This is the 'Hathor incident,' which the Colonel has asked me never to discuss." Similarly, the first season episode Emancipation is also frequently overlooked and seen as one of the worst episodes by both the cast and production team.
SG-1 recast every character from the original Stargate with the exception of Daniel's brother-in-law Skaara (Alexis Cruz) and father-in-law Kasuf (Erick Avari). Lampshaded when O'Neill is mistaken for another soldier with the same name (except that it's spelled O'Neil) and he remarks that the other one had no sense of humor.
Post-Script Season: The show was expected to be cancelled after five seasons, and so ended on a decent (but not Grand) finale ("Revelations") — the expectation was that they would then move on to The Movie (to be called "Stargate: The Lost City" or something similar) which would segue into the Spin-Off (Stargate Atlantis, which was very different in concept at this stage). Then the show was renewed for a sixth season, and so was given a Grand Finale ("Full Circle") which introduced the planned concept of The Movie. Then the show was renewed for a seventh season, so The Movie was cancelled and its concept was rewritten as a season-long arc that would finish with a two-part Grand Finale ("Lost City") which would segue into the Spin-Off instead. Then the series was renewed for an eighth season, so the Grand Finale's ending was changed to make more of a cliffhanger to be resolved in the Season 8 premiere, and Stargate Atlantis started running concurrently to Stargate SG-1. It was expected that the eighth season would be the last, however, so the end of the season was once again devised to close the book on the series: both major galactic threats were taken away in a three-episode arc ("Reckoning" Parts 1 & 2 and "Threads" — interestingly, these came just before the Grand Finale), and then the series ended with yet another two-part Grand Finale ("Moebius") involving time-traveling to ancient Egypt. The show was then picked up again for a ninth season, and was given a retool which replaced several cast members and introduced a new Big Bad. Season 9 was made knowing that the show would be renewed for at least another year — and then, finally, the show was cancelled after the end of Season 10. Whether the final episode ("Unending") was a Grand Finale is doubtful; the real resolution of the series happened in the DVD movie The Ark of Truth. And then there was another DVD movie, and more planned... until Stargate Universe underperformed. Ooops.
Vaitiare Bandera (Sha're) was married to Michael Shanks (Daniel Jackson) in real life, and was pregnant with his child when her character was written as carrying Apophis' son.
Michael Shanks got appendicitis during the filming of "Nemesis", so Daniel Jackson was written out of most of the action in that episode and "Small Victories" by also giving him appendicitis.
Carter temporarily changed her primary weapon from the P90 to the custom-built "Carter Special" starting in the middle of season 7 because the show's suppliers ran short of P90 blanks during the invasion of Iraq.
At a convention panel, actor Don S. Davis (General Hammond) was asked what role he would play if given a choice of switching characters, and he responded that he would play his own role since he had the best chair on the set. When Hammond returned in "Prometheus Unbound" after he was promoted away from the SGC, he made a point of taking the chair with him when boarded the Prometheus.
Vala's pregnancy in season nine stemmed from Claudia Black's real-life pregnancy.
Sergeant Siler is routinely battered throughout the series, from being a test target for new staff-weapon armor, to having a DHD blow up in his face. At first glance it's just a running gag, like Daniel dying and coming back to life all the time, but then you see the credits and find out that Dan Shea, the actor that portrays the good Sergeant, is also the stunt coordinator. Also, Shea was Richard Dean Anderson's stunt double in both MacGyver and SG-1.
Lexa Doig, who played Dr. Carolyn Lam in season 9 and 10 is Shanks's second wife.
The DeLuise brothers, Michael, Peter, and David, all worked on SG-1 in various roles (directors, producers, writers, and actors at various times). Their father, comedic actor Dom DeLuise, guest-starred as the title character in "Urgo" (and at one point transformed himself into a stuffy Air Force officer played by Peter).
Talking to Himself: Michael Shanks voices several Asgard, including Thor, so whenever one of them and Daniel Jackson are talking to one another, it's an example of this. Lampshaded when speaking to Kvasir, Daniel dryly comments he misses Thor.
Most of Jack O'Neill's snarking for the first couple of seasons was improvised by Richard Dean Anderson, after which the writers gave up and started writing it into the scripts.
Samantha Carter's line in "Children of the Gods" about how the SGC's gate control computer had been MacGyvered from three supercomputers was an ad-lib Amanda Tapping came up with during her audition.
The concept of Jaffa performing a meditation called "kel'no'reem" was apparently inspired by Christopher Judge falling asleep on set during a take, and Michael Shanks quipping "Oh, he's not sleeping, he's meditating."
The Romance Arc between Jack and Sam started with an exchange in "Solitudes" that was ad-libbed by RDA and Tapping. Trapped in an Antarctic ice cave, they snuggle together for warmth.
Most of the dialogue of the title character in "Urgo" was ad-libbed by Dom DeLuise. Part of the reason why he has so few scenes where he's in frame with Christopher Judge is that the latter had trouble keeping Teal'c trademark stoic attitude around the former.
Un-Canceled: From season six through season eight, the showrunners were in constant fear of cancellation and, unlike previously where the season finale ended on a cliffhanger, closed out the season's arc solidly. And yet Sci Fi Channel kept renewing it, continually derailing plans for a Grand Finale film (a fact referenced by "200"). And then just as the showrunners decided they could keep going, the network ended the series.
Apparently, there were plans to make Adria more long-lasting, including having her fuse with a Goa'uld symbiote. However, plans fell through after Sci-Fi ended the series, and instead had her do a re-hash of Anubis's final plot. The Goa'uld symbiote part actually happened in abbreviated form, resulting in Adria having to Ascend to a Higher Plane of Existence after a failed extraction attempt killed the symbiote but left her dying.
After the series ended the plan was to do one or two movies a year for both SG-1 and Stargate Atlantis, but according to the producers the bottom fell out of the DVD market and Sci Fi balked at continuing after the first two. Apparently the third movie, entitled Stargate: Revolution, would have featured Jack's return as the main character and it would have finally had the Stargate program going public. However it can be considered shelved for good at this point.
A tie-in first person shooter video game was in development at one point. Footage from the beta version appeared in an actual episode as part of a computer simulation combat model, but it was eventually cancelled.
With Lyrics: The theme song was given lyrics in the DVD commentary for "Prodigy", sung by the producers.
Various writers and producers (and a Deleted Scene from Stargate Atlantis) have all said that Jack and Sam became a couple offscreen after Jack was promoted out of the SGC and her direct chain of command.
Joseph Mallozzi says of an exchange in "The Scourge" where Daniel and the Chinese representative start making fun of him in Mandarin, that Cam Mitchell doesn't actually speak fluent Mandarin. He just knows how to say "Screw you!" in Mandarin, and happened to guess right that time.
Word of Saint Paul: The finale of the series contains a long Time Passes Montage with little to no dialogue throughout. Several of the actors involved have given their take on what happened — such as Amanda Tapping and Chris Judge saying they played their parts as if Sam and Teal'c had developed a relationship, and Michael Shanks saying the reason that Vala is crying and being consoled by Daniel in one scene is because she miscarried.