Between the episodes Small Victories (2000) and Redemption: Part 2 (2002), the Beta (Antarctic) stargate is used at the SGC for gate travel, since the original gate ended up at the bottom of the Pacific Ocean in "Small Victories" and later fell into the possession of the Russians until its return to the SGC in "Redemption Pt 2". In Solitudes (1998) (the first episode to feature the Beta gate), the point of origin symbol (an octagon with a line below it) is different from the point of origin symbol of the original gate (pyramid and circle); however, in various episodes that featured the Beta gate in use, the point of origin symbol mysteriously changes to the symbol from the original gate.
Before going to a new planet a MALP (or FRED) is sent through with supplies, cameras, atmospheric sensors but they rarely bring it back with them when they leave.
Throughout the series, the length of time a wormhole (the 38 minute limit not withstanding) varies regardless of what gate. There are times a gate will stay active for several minutes waiting on various people to finally mosey up to it. Other times, particularly when the bad guy is seconds behind, the gate will shut down immediately after the last of our SG1 heroes jumps through.
The characters of Kasuf, Skaara and Sha'Re (originally from Stargate (1994), the movie this series is based on) appear through the series in various episodes. In the movie, all three characters spoke virtually no English whatsoever, however in the TV series (in which the First Season is set one year after the movie) all three speak perfect English. It is possible that Daniel Jackson taught them English during the year-long span between movie and TV series, but it is highly unlikely they learned it so well in such a short span of time.
Jack O'Neill is a flag officer in the USAF and thus deputy commander of the Stargate program. This means that he would have an organizational rather than an operational role in the unit. He would not be allowed to go on most missions as his knowledge and expertise would have been exploited by an enemy were if he was captured.
The very idea that most alien civilizations outside of Earth can speak English is a linguistic impossibility. English was developed long after the stargates were used to populate these other planets and furthermore, English is an amalgamation and evolution of other early languages unique to Earth after the Gou'ald. Nevertheless, production logistics and writing logistics made it more practical for alien encounters to speak English as to eliminate the repetition of Daniel deciphering the language and then translating the language to the rest of the team for any episode dealing with an alien race which were the majority of the episodes. This also helped eliminate the need for the writers to invent a new language for every new alien civilization encountered. This practice carried over into Stargate: Atlantis as well.
The IOC ( International Oversight Committee) as explained makes little sense. The US can clearly afford to maintain the Stargate program and giving countries which might someday be enemies of the country access to a technological advantage could threaten national security. While it was done to give the series a broader appeal, overall the ideas behind it don't match up with the logical flow of the narrative. However, considering the vagaries of international diplomacy, it is certainly possible.
There are a total 39 symbols on any Stargate; 38 that are on every gate and 1 that is unique to the specific gate (point of origin) and addresses have 6 symbols plus the point of origin. The dial home devices all only have the 38 symbols and a center "enter" button which would serve as the point of origin. Despite this, throughout the entire series, any time someone was seen or heard using a DHD, they always press 7 buttons before hitting the center button instead of 6.
Whenever a call comes in to a gate, the wormhole first splashes out a few feet before the flat "puddle" is formed. Anything caught in the splash is completely annihilated. It makes no sense that the gates have no safety cages, railings or at least simple floor markings to outline the danger zone.